He's well within his rights to stay and fight for his place, but I just gotta say this....you dumb, dumb guy.
His contract runs out in 2021 and Barcelona are NOT offering him an extension. If he leaves to PSG, Inter or Juventus, he can get one final big contract and paycheck. If Barca are serious about wanting to move on from him, he's not going to get many minutes this season anyway so his fight for his place will be for nothing, and he'll just devalue what he could demand in negotiations from a new team next year.
I have no sympathy for Rakitic, he's been talking trash in the press for two years now trying to put pressure on the club into giving him a fatter contract and saying shit like "My position is already taken" when asked about de Jong and competition for starting spots. Valverde spoiled him starting him no matter what and he thought he was untouchable.
That said, he doesn't deserve the shit that's thrown to him and his wife on social media platforms. That's awful.
Remember Rabiot's story:
If you are free, you can get higher wages.
If Barca had to pay 50M transfer fee for Rabiot, they would offer only let's say 6M wages.
If Rabiot is free, we don't have to pay any transfer fee and he can ask for 10M and even a sign on bonus.
According to internet, he is earning 8,6M per year at Barca, probably Net, right?
That's quite a lot.
For 2 years at Barca, he will earn 17,2M Euros.
And even then, he will be free and aged 33.
He can still sign 1-2 years deals with Inter, Roma, Milan for let's say 3-4M per year since he is free and they can give him decent wages.
So, if he'll stay 2 years at Barca and 2 years at Milan, he will earn 8,6+8,6+3,5+3,5=let's say 24,2M Euros, and he will live for two years at Barca and he will be able to pick his final destination.
On the other hand, if you force him to Juve, I don't believe that Juve would give him 8,6M wages as Barca.
Let's say that Juve would give him 7M for 3-4 years.
Ok, he would earn slightly more (if they would offer a 4 years contract), but he would be forced to live in a city which he and his wife don't like.
Also, there is always a chance that someone like Psg or EPL clubs will offer him 4-5M when he will be free, so he will earn equally as he would earn with moving to Juve today.
Not to mention that Barca surely has some crazy rich bonuses.
And since we will probably win 2 La Ligas in the next 2 years.
And maybe one CL (who knows?), there is a chance that he will earn additional 1-2M from Barca's bonuses.
My point: staying at Barca, and even not playing, is probably the most lucrative offer in the world.
Especially if you like a club and a city.
Some will reply: his career will die.
Well, he is 31 years old already.
Even if his career dies, so what?
And he probably believes that he can regain his spot during a season.