And Mikel Arteta’s side could move to replace him with Wolves midfielder Ruben Neves.
Xhaka has been a key player since for the Gunners since joining from Borussia Monchengladbach in 2016, establishing himself as a regular under Arsene Wenger, Unai Emery and current boss Mikel Arteta.
The 28-year-old was a mainstay in midfield under Arteta this season, also filling in at left-back while Kieran Tierney was out injured.
But he is close to agreeing a permanent transfer to Roma ahead of next term, according to Football London.
The Gunners are believed to be keen on Neves as a potential replacement – and The Telegraph claims they will make an opening offer this week.
But Wolves will demand at least £40million for their midfield star.
Xhaka is understood to be happy in North London, but is drawn to the prospect of playing under Mourinho.
The midfielder has often been criticised by fans during his time with the Gunners – but was praised by Mourinho back in 2019.
“Xhaka is the main man in the entire Arsenal midfield, you can’t see it unless I lend you one of my eyes,” said Mourinho, who has previously tried to sign the Swiss ace.
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“Without him, Arsenal is lost. He is a leader. Remember, mistakes are made by humans.”
Now it seems as though the two could finally be united as Mourinho looks to make his squad more competitive in Serie A next season.
Xhaka looked set to leave Arsenal in January last year, having agreed terms to join Bundesliga side Hertha Berlin, but was persuaded to stay by Arteta.
The midfielder had been stripped of the captaincy by Emery after an outburst at Gunners fans when he was hauled off during a draw against Crystal Palace at the Emirates in October 2019.
Xhaka was left out of Arsenal’s next three Premier League games, but was reintegrated into the side under Arteta after took charge following Emery’s sacking.
Arsenal are looking to raise in excess of £60million with player sales this summer, having already missed out on Emi Buendia after Aston Villa agreed a deal for the Norwich midfielder.
The Gunners remain locked in talks with Real Madrid over the signing of Martin Odegaard, whose future is uncertain after Los Blancos appointed Carlo Ancelotti as manager last week.