The Northern Ireland international came through the youth system at Man United and went on to represent their first team on 198 occasions, winning three Premier League titles, the Champions League, two League Cups, four Community Shields and the Club World Cup during his time at Old Trafford.
Evans departed for West Bromwich Albion in 2015, spending three years with the Baggies before moving to Leicester, and he represented the Foxes on 152 occasions before leaving on a free transfer.
The 35-year-old has been pictured arriving at Man United's Carrington base, and according to the Manchester Evening News, he has been training with the club for the past week.
The report claims that Evans is currently considering his options for the new campaign, although there are no indications that he could re-join the 20-time English Champions.
The experienced defender has allegedly been training with the academy and the first team, with Man United pleased to have his 'quality and experience' as part of the group.
Evans struggled with a calf problem during the 2022-23 campaign, which restricted him to just 14 appearances in all competitions, and he did not sign a new deal with Leicester.
The centre-back is thought to be keen to remain in the Premier League, with Everton said to be in the hunt, and he has vast experience in England's top flight, featuring on 356 occasions in the competition.
Man United have released Phil Jones and Axel Tuanzebe this summer, while Eric Bailly is also expected to depart on a permanent basis, meaning that, in theory, there could be a spot in the squad for Evans if the Red Devils decide to bring him in for next season.
Harry Maguire is also being heavily linked with an exit, with the club captain not in the plans of head coach Erik ten Hag for the 2023-24 campaign.
Man United started their preparations for the new season with a 2-0 victory over now Championship outfit Leeds United last Wednesday.
The Red Devils will be back in action against Lyon on Wednesday before heading to the United States for their pre-season tour.
Bruno Fernandes, Casemiro and Marcus Rashford were among the players to train with Man United on Saturday, with the majority of the club's first-team stars returning later due to their international commitments.
However, it is again expected to be largely a youthful squad against Lyon, with Ten Hag wary of rushing those back who have only just returned to team training.