The Gunners are looking to improve their squad this summer.
And they have already been linked with moves for stars such as AC Milan’s Franck Kessie.
The latest name to emerge is Under, who helped Roma to a Europa League qualification spot.
The Turkish international scored six goals and made 11 assists last season.
Under also added to his international tally with a goal against World Cup winners France on Saturday night.
This form has sparked interest from the north London side, according to Turkish-Football.
And Robbie Lyle, host of popular fan show AFTV, has backed a move for the 21-year-old.
The Under speculation comes as:
The host said: “He’s been doing bits for Roma.
“We saw it last night in a great goal but he was also instrumental in everything good Turkey did.
“At international level, he was taking all the set pieces.
“He looks a really good player. Now we see why Arsenal are in hot pursuit of him.”
But the host believed there could be a problem with pursing this star.
“His valuation is £44million,” Lyle added.
“And his valuation might have gone up.
“He’s on really low wages, though, at £15,000, so Arsenal could treble that.
“But will we be able to meet that sort of price?
“Arsenal wanted him January but didn’t have the funds. We were told the summer would have loads more funds.”
“His valuation is £44million but will we be able to meet that sort of price”
Robbie Lyle, AFTV host
And the Gunners faithful were left concerned about the Turkish star’s price tag.
“Arsenal can’t afford him,” one supporter said.
Another commented: “Arsenal will got for a b-tech version of Under.”
While a third simply said: “He won’t come.”
It comes as a transfer agreement was agreed for one star last summer.