However, the Spain international is not keen on leaving the La Liga club anytime soon and has rejected the offer.
Barca are also not interested in losing Fati with Ousmane Dembele on his way out, and they have also knocked back the proposal from Arsenal.
The Gunners want to add a forward to their ranks this summer, and it appears they are now desperate to land one after Gabriel Jesus underwent surgery last week.
The Brazil international striker is out of action for a few weeks as a result, and Arsenal could do with bolstering their attack with a quality forward right now.
Fati has played on the wings and even as a number 9 for Barca and could have been a solid addition for the Gunners.
He struggled for regular minutes last term and he knows he has a chance to establish himself in the starting XI with Dembele on his way out.
The North London club will need to look elsewhere for the forward they want as the Spaniard clearly is not looking to leave Camp Nou this summer.
Arsenal were linked with the 20-year-old earlier this year after his representatives opened the door for a Barcelona exit following his struggles to break into the starting XI.
However, the La Masia academy graduate is set to remain at the club, but he could be available again if he fails to force his way into the plans of manager Xavi.
Arsenal need quality squad depth this term if they are to challenge for the Premier League title, and while scoring goals is not a problem for them, adding a player capable of finding the back of the net regularly would not hurt.
Manager Mikel Arteta will hope that the likes of Eddie Nketiah, Kai Havertz and Leandro Trossard can step up in the absence of Jesus and get his side firing on all cylinders as they look to hit the ground running in the new season.
