The Sun, as quoted by the Daily Mirror, is reporting that the Gunners are interested in a potential summer swoop to sign the 21-year-old to help Unai Emery bolster their midfield.
The same article states that Arsenal have sent scouts to watch the Turkey international represent AS Roma in the current campaign.
According to the same story, the north London side may have to produce a fee in the region of £30m to sign the Turkish winger in the summer.
The report goes on to say that Under’s current valuation would represent 75 per cent of Emery’s summer transfer budget.
Arsenal were 2-0 winners against Manchester United in the Premier League at The Emirates last weekend to seize control of the top-four race.
Goals from Granit Xhaka and Pierre-Emerick Aubameyang allowed Arsenal to hoist themselves above Manchester United and into fourth spot.
Emery could have more transfer funds available if the Spanish head coach is able to steer Arsenal back into the top four in his first season in charge.
The north London side will be hoping to overturn a 3-1 first leg deficit against Rennes in the return fixture at The Emirates in their Europa League last-16 tie on Thursday night.
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