Manchester United could have been the club to sign Gyokeres from Sporting CP, but since he made it known that he wouldn't join Manchester United, that made Manchester United not to enter the race to sign Gyokeres, and that's also the reason why Arsenal was able to sign Gyokeres. Arsenal was very serious about signing Gyokeres, but since Sporting CP used Manchester United to raise Gyokeres's transfer fee, Arsenal found it difficult to meet Gyokeres's transfer fee fast.
That is not the case, Gyokeres was interested to play in the champions league, and Manchester united are not in any Europe competition this season. No striker of his level will play for a club that is not in Europe competition, is not that he rejected Manchester united, he needed to play in champion leagues that is why he chosen Arsenal over Manchester united.
Arsenal was not much interested, it was the player that forces the transfer to Arsenal. Manchester united offer was better than what Arsenal offered him. But the player choice must be respected. Gyokeres is not ready to build a team with his former boss Ruben Amorim at Manchester united, he wanted to already made team, like Arsenal who was lacking a top striker. I wish him well as a Manchester united fan.