According to Gazzetta dello Sport, Xhaka has already agreed personal terms with the Serie A side, but they are yet to meet Arsenal’s valuation of the midfielder.
Since being appointed as Roma’s manager at the start of May, Jose Mourinho has focused on strengthening his squad with new signings.
Xhaka was quickly identified as someone whose leadership and battling qualities would help to reinforce the club’s midfield following a disappointing seventh-place finish last season.
After losing 12 games and conceding 58 goals, the most of any team in the top half, Roma ended up 16 points behind Juventus, who occupied the last Champions League spot.
Although Xhaka is keen to leave the Emirates in search of a fresh start, Arsenal are determined to recoup as much of their original fee as possible.
They paid Borussia Monchengladbach £35million for the Swiss international in May 2016, but his form in the Premier League has been patchy.
Some undisciplined and error-strewn performances have contributed to a tempestuous relationship with the Arsenal supporters.
Xhaka was infamously jeered by some when he was substituted against Crystal Palace two years ago, and his frustrated reaction only inflamed matters further.
He has two years left on his contract and would welcome the opportunity to kickstart his stalling career in Italy.
The 28-year-old was in superb form for Switzerland at the Euros as they unexpectedly reached the quarter-finals before losing on penalties to Spain.
Meanwhile, Roma have agreed a fee with Wolverhampton Wanderers for Rui Patricio, who is expected to complete his move later this week.
The experienced Portuguese goalkeeper has spent the last three seasons with Wolves, having joined the club from Sporting CP.
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