Hence, the bolded. 

Sony probably wouldn't have enter the console market.

They offered the PlayStation to Nintendo.

Nintendo refused because it was CD based console.

We all know what happened afterwards :)

Nintendo would have probably had squaresoft on its side and the rest of Japanese 3rd party follow suit. Then n64 would have sold more than playstation..

Playstation wouldnt exist today if N64 was CD based.

Nintendo & Sony were in partnership developing a CD drive for the SNES, if it wasn't for Nintendo Sony wouldn't have started development on the PS1 at all. There was no "offering" as if Sony spent millions developing PS1 and thought "let's give it to Nintendo"

There were disagreements about something during development, I can't say for sure who at fault is for that (I think Nintendo disliked some clauses about licensing Sony wanted for any games made for the CD drive, and Nintendo 'went behind their backs' (in quotes because I doubt it was actually a fully secretive move as it would have been illegal) to make a partnership with Panasonic Phillips [oops, thanks Justinian] instead.

After that, Sony continued developing the CD drive until they released it as the Playstation. Then due to a number of factors: Sony's loss leading strategy, CDs being cheaper to print, Sony's EU infrastructure/Nintendo's ignorance of European demand, CDs capable of holding FMVs, moneyhatting, plus Nintendo's seal of quality which probably prevented a lot of smaller companies releasing games for SNES/N64 at all. PS1 eventually won out.

Then it would have been the best console of all time, horrid patience testing load times and rampant piracy disregarded. -_-
But seriously can you imagine most of Square's Golden Age offerings on N64 instead? FF7 and FF8, Xenogears, FF Tactics, Chrono Cross, Bushido Blade, Einhander, Vagrant Story. The only reason they left in the early days was storage space, and maybe some money-hatting, who knows.

Damn. We'd be in a different world.
But of course the whole CD debacle with the SNES is the reason why PS exists in the first place. If Nintendo was going to have a CD system that's the way it would have happened. If Nintendo could just work out a proper licensing thing with Sony at the time... If there's one alternative history I'd want to see play out in this industry it's definitely that one.

They maybe would've been able to money hat some titles like Tomb Raider and Tekken, but Nintendo retains Final Fantasy and Dragon Quest and everything else goes multiplat with the N64 having better versions of many games due to stronger hardware. 

The N64 actually had pretty darn good Western developer support as is even with the terrible cart format; Turok 1/2/3, Beetle Adventure Racing, 007: The World Is Not Enough, Star Wars Episode I Racer, South Park 64, DOOM 64, WCW/NWO games, NFL Quarterback Club, Body Harvest (from the future GTA3 devs), Space Station: Silicon Valley, Rocket: Robot on Wheels (now the developer of inFAMOUS), Star Wars: Rogue Squadron, Starcraft 64, Top Gear Rally, etc. 

A lot of Western devs were pushing it harder than the PSX, like higher resolution games than on the Playstation. 

EA actually got on board with the N64 because Howard Lincoln went to bat for Nintendo and assuaded them to make games on the N64 even though they didn't like the cartridge medium, but he wasn't going to take no for an answer. He also insisted that Nintendo also invest in more sports games like NBA Courtside featuring Kobe Bryant ... this back when Nintendo of America had competent leadership that actually had authority to do things. 

If Nintendo retains the Final Fantasy and Dragon Quest franchises by going CD, then Sony would've been screwed. The other Japanese devs, whether they liked Nintendo or not would have to fall in line. Honestly in the early years of the PSX they didn't spend heavy resources on it because they didn't know if it would be a hit or not, the N64 sold like wild fire at launch, the PSX had a much slower ramp up. 

Nintendo wins that easily. Playstation circa 1996 is not the Playstation brand that it became later on and GoldenEye was a huuuuuuuuuuuuuuge find in the West, it's the forfather of the Call of Duty phenomenon except Nintendo had it exclusive to themselves. 

Sony wanted to have all rights for merchandising articles, too. This included all Mario and Zelda merchandising. That was too much for Nintendo and so they didn't accept the CD add-on of Sony for the SNES and separated. Then Sony decided to make an own console (PS1).

Nintendo preferred to use cartridges because of the fast start of the games and no loadings. Isn't it great to put a cartridge into a console and immediately start gaming? That's something I miss since optical discs. By the way, no loading screens were also the reason for Nintendo to use mini DVDs for the Gamecube. Everyone sees the disadvantage of less memory capacity and no one the advantage of faster data access...

Just compare the loading time between battles in Final Fantasy VII, VIII and IX on the PS1 with FF IV, V and VI on the SNES (yes, the technical data of the SNES are more comparable with the PlayStation than the N64). Nintendo never wanted to have the best graphics or FMVs – they wanted to have the best gameplay and fun in the games. That's why they prefer fluent frame rate instead of HD graphics.

The success of the PlayStation was not (only) caused by the quality of the games, but everyone had a chip in their PS1 console and copied the discs and so they reached many people. That wasn't possible on the N64. I think Sony wasn't happy about that circumstances, but nevertheless the PS1 was a big success for Sony.

I still don't think it was a failure of Nintendo to prefer cartridges in the gameplay point of view. No one could have forecast the success of the PS1. The Sega Saturn had also discs and had no success.

Sony Playstation would never had released if that happened...

If the 64 used disks instead of cartridges the Nintendo Playstation would still be the dominant console today.