And it appears as though the capital club do not fear a scrap over their star man.
According to Corriere dello Sport, Arsenal saw a £54m (€60m) bid refused by Roma’s transfer strategist Monchi.
Monchi used to work with current Arsenal boss Unai Emery at Sevilla and masterminded a number of big moves during his time there.
He switched to Roma in 2017 and has been tasked with recruiting a new generation of stars to the Stadio Olimpico.
Arsenal transfer news: Roma have rejected a bid for Cengiz Under (Image: GETTY)
Arsenal transfer news: Roma seem determined to keep Cengiz Under (Image: GETTY)
Arsenal transfer news: The Gunners may not make another bid for Cengiz Under (Image: GETTY)
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Asked about Under’s future in November, Monhci said: “We haven’t decided anything for Cengiz Under yet.
"He is very young, he is improving.
"But this is not the right moment to discuss a new contract and he must continue the growth process.
“Let’s leave him in peace to mature at his own pace. What needs to come will come in good time.”
Roma: Cengiz Under shows off impressive skills against Verona
Arsenal are seeking midfield reinforcements with the knowledge that Aaron Ramsey is set to leave the club.
A contract with the Wales international has not been agreed on and he is set to sign a pre-contract deal with Juventus this month.
It would mean Ramsey leaving for nothing at the end of the campaign but the club are refusing to accept his wage demands.