Both Premier League giants are targeting the Sweden centre-forward.
The Sun says United are still favourites for the moment, with the aim to sign Gyokeres this summer.
The presence of Ruben Amorim on the United bench has Gyokeres leaning towards a move to Old Trafford, given the two men shone together at Sporting.
But United will have to face competition from Arsenal. After the injuries of Bukayo Saka and Gabriel Jesus, the Gunners are seeking to strengthen their attacking options this month, with Gyokeres high on the agenda.
The player has a release clause of €100 million, but that could be revised downwards this summer.
