The 26-year-old is set to leave the Emirates Stadium on a permanent basis this summer having previously revealed that "there is no chance" he will be staying in North London, although his agent has stated that the midfielder will be part of the club's pre-season tour of the USA.
Even though a permanent move to Fiorentina, where Torreira spent last season on loan, has failed to materialise, there is a "possibility" that the Uruguay international could remain in Italy with Roma.
When asked by reporters in his homeland about a potential switch to the Giallorossi, Torreira said: "Roma? Yes, there is a possibility. I spoke to Mourinho a while ago. I admire him as a coach. It's an opportunity that tempts me a lot, but it's not easy."
Torreira, who cost Arsenal £25.8m to sign from Sampdoria in 2018, has made 89 appearances across all competitions for the Gunners, but his last game in red and white came back in July 2020.
Another Uruguayan who is on the lookout for a new club is veteran striker Luis Suarez, who is currently a free agent after his contract with Atletico Madrid expired last month.
The 35-year-old is hoping to sort out his future quickly and play regularly ahead of representing his country at the 2022 World Cup in Qatar later this year.
While Suarez has been linked with the likes of Aston Villa and River Plate, the striker has revealed that he has received 'several contract offers' from MLS clubs, although he is currently sceptical over a proposed switch to the USA this summer.
Speaking to Radio Sport 890, via Goal, Suarez said: "The thing is that some possibilities are for January, I have to analyse everything. The market in MLS is very complex.
"Some clubs want you but they don't have the slots, and so it would have to be for January. Other clubs want you now but I have to evaluate if they have a chance to qualify for the playoffs.
"I'm not closing the door to anyone and I've listened to all the offers. But if some MLS teams don't qualify for the playoffs, they end their season in the first week of October, and that's not useful for me because I would stop for a month ahead of the World Cup, which wouldn't be good for me."
Suarez, who has spent the last 16 years of his career playing in Europe, made 45 appearances in all tournaments for Atletico last season, scoring 13 goals and providing three assists.
Back in the Premier League, Everton are reportedly interested in signing Chelsea midfielder Conor Gallagher this summer.
The 22-year-old enjoyed a successful 2021-22 campaign on loan with Crystal Palace, where he recorded eight goals and five assists in 39 appearances across all competitions.
Gallagher has since returned to Chelsea and has been included in Thomas Tuchel's 29-man squad for their pre-season tour of the USA.
However, i reports that Everton boss Frank Lampard is exploring the possibility of signing Gallagher on either a loan or permanent deal.
The report adds that Lampard's former club Chelsea will leave it late in the transfer window before deciding whether to let the English midfielder leave Stamford Bridge.
Everton are also closely monitoring Gallagher's teammate Armando Broja, while that have allegedly had a £25m bid for Morgan Gibbs-White rejected by Wolverhampton Wanderers.
Elsewhere in the English top flight, newly-promoted Fulham have reportedly made an enquiry over the availability of Crystal Palace midfielder Luka Milivojevic.
The Cottagers have already bolstered their midfield options this summer with the permanent arrivals of Joao Palhinha and Andreas Pereira from Sporting Lisbon and Manchester United respectively.
However, the Daily Mail reports that Marco Silva's side have approached Palace over a proposed move for Milivojevic, who has just 12 months remaining on his contract.
The 31-year-old Serbia international struggled for game time under new boss Patrick Vieira last season and started only nine times in the Premier League.
Milivojevic, who has spent the last four-and-a-half years at Selhurst Park, was once viewed as a key asset in the Eagles midfield, but if he is to remain a peripheral figure under Vieira then a potential switch across London to Craven Cottage could be on the cards.