Former Tottenham manager Mourinho was appointed as Paulo Fonseca's replacement at Roma shortly after he was dismissed by Spurs in April, with his contract starting ahead of the 2021-2022 campaign.
Yet speculation is already rife that Xhaka, Arsenal's former club captain, is one of Mourinho's priority transfer targets.
Xhaka has spent five seasons at Arsenal since joining from Bundesliga club Borussia Monchengladbach, though the Switzerland international has not always been a popular figure with the club's fanbase.
Nevertheless, he has featured consistently in the first team under Arsene Wenger, Unai Emery and Mikel Arteta, and the 28-year-old – who played more minutes in all competitions last season than any other Arsenal outfield player – still has two years left to run on his contract.
Xhaka is already with the Switzerland squad as they prepare for Euro 2020, and pressed on his future, he told Swiss-German publication Blick: "Of course I read the rumours too. But now I'm one hundred per cent focused on the national team.
"That's more important than Arsenal or rumours right now. I still have a two-year contract in London, and at Arsenal they know what they have got in me. When the time comes and we can, and may have to talk about a transfer, I'll be there."
Asked to comment on what Mourinho's reported interest means to him, Xhaka added: "Honestly, I didn't hear what Mourinho said, but that makes you proud.
"Everyone knows Mourinho, knows what he has achieved. Mourinho knows how to win titles. You can now see what work I have done over the past few years.
Xhaka scored one goal in 2020-2021, providing two assists and creating 20 chances in total, with all of those opportunities coming in open play.
Roma would also benefit from Xhaka's consistent availability. Of Arsenal midfielders, only Bukayo Saka (46) made more appearances than Xhaka in all competitions.
Bryan Cristante (48), Lorenzo Pellegrini, Gonzalo Villar (both 47) and Henrikh Mkhitaryan (46) ranked ahead of Xhaka for appearances in terms of Roma midfielders, but the Swiss started more games than any of them (42).
Xhaka's passing accuracy of 89.89 per cent ranks him third out of Roma and Arsenal midfielders to play at least 10 times across all competitions, with only Mohamed Elneny (92.08) and Martin Odegaard (90.38) bettering his success rate.
It is Xhaka's defensive work that perhaps goes under the radar, especially with his tendency to lunge in recklessly, a trait that has seen him receive three straight red cards in his Arsenal career, but he is far clear in the recoveries rankings, having regained possession 281 times in 2020-21, with Cristante (235) Roma's best player in that regard.
Only Mkhitaryan (75) went in for more tackles than Xhaka (74), though his tackle success rate was down at 50 per cent, lower than 10 other Arsenal or Roma midfielders who have played at least 10 times last term.