The Red Devils welcomed the 37-year-old back to Old Trafford for a second spell last year, and he enjoyed a strong campaign at an individual level with 24 strikes from 38 matches in all tournaments.
Ronaldo found the back of the net 18 times in the Premier League, but his efforts could only help the 20-time English champions qualify for the Europa League in sixth place.
In spite of the arrival of Erik ten Hag, Ronaldo is understood to have told Man United that he wants to leave in the current window amid fears that he will not be able to fulfil his silverware ambitions at Old Trafford.
Man United have no intention of parting ways with the five-time Ballon d'Or winner, who has another 12 months left on his contract with the option to extend until the end of the 2023-24 season.
However, Spanish outlet AS claims that Barcelona are also interested in signing the Portugal international, in spite of his association with bitter rivals Real Madrid.
Ronaldo spent nine years on the books at Real Madrid, winning four Champions Leagues and scoring 450 goals in 438 appearances before leaving for Juventus in 2018.
The report adds that Mendes has now met with Barcelona president Joan Laporta, during which the pair floated the idea of a sensational switch to Camp Nou for Ronaldo while also discussing other players.
Barcelona president Laporta allegedly wanted to bring Ronaldo to the club in 2021 amid his then-uncertain future, but Barcelona's long-running financial problems made a deal impossible.
Ronaldo was due to return to Man United for pre-season training on Monday but was absent due to family reasons, and the likes of Paris Saint-Germain and Sporting Lisbon have also been linked with a move for the attacker in recent days.
Bayern Munich were also tipped to move for Ronaldo amid Robert Lewandowski's desire to leave and play for Barcelona, but the Bundesliga champions are not thought to be interested in a move for the Portuguese.
A separate report from The Athletic states that former Red Devils interim boss Ralf Rangnick approached football director John Murtough and CEO Richard Arnold with a proposal to sell Ronaldo in January, but the two club chiefs refused to sanction a move.
Should Ronaldo ultimately elect to stay at Man United, the forward allegedly believes that the club need to make at least six new signings in the summer transfer window to compete for silverware.
Ten Hag's side will commence their pre-season tour in Thailand next week, and the club have reportedly informed Ronaldo that he will be required to attend the tour.