The Arsenal youngster is currently on loan at Leeds, but is yet to start a Championship game under Marcelo Bielsa this season.
Nketiah, who has scored four goals in nine games, is behind Patrick Bamford in the pecking order.
The Sun claim Arsenal could recall the striker in January and send him on loan to Bristol City, who tried to sign him in the summer, in order to improve his playing time.
The Robins are in need of firepower after losing on-loan Stoke forward Benik Afobe to a season-ending knee injury last month.
Nketiah, 20, could significantly strengthen Bristol City’s promotion push as Lee Johnson’s men sit sixth in the table after 11 games, below Leeds on goal difference.
Leeds managing director Angus Kinnear appears confident of keeping Nketiah at Elland Road beyond January.
He told the Talking Shutt podcast: “It’s fairly standard in these contracts to have January recalls but the decision is based on how well the loan’s going so if the players are playing, and they’re playing well.
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