David de Gea is again expected to be the team's number one next term under new head coach Erik ten Hag, and the Spaniard's current back-up Dean Henderson is believed to be on the verge of joining Nottingham Forest on loan for the 2022-23 campaign.
Tom Heaton is still at the club, but Lee Grant has retired this summer, meaning that the 20-time English champions will need to move for another stopper if Henderson departs.
According to the Manchester Evening News, Romero is open to returning to Old Trafford, just one year after leaving the club on a free transfer.
The 35-year-old spent the 2021-22 campaign with Venezia in Serie A, making 16 appearances, but he missed a lot of football in the second half of the season due to a serious knee injury.
The 96-time Argentina international's contract at his Italian club is due to expire at the end of June, and he is leaving on a free transfer this summer.
Man United are allegedly yet to signal a solid interest in Romero, but the experienced goalkeeper has made it clear that he would be open to returning to Old Trafford ahead of the new campaign.
According to the newspaper, Romero has a lot of love for the club that he represented between 2015 and 2021 and "would always come back" if he were approached.
The South American arrived at Man United on a free transfer in 2015 following his exit from Sampdoria, and he went on to make 61 appearances for the club in all competitions.
Romero's most productive campaign came in 2016-17, when he featured on 18 occasions in all competitions, but he only made seven Premier League appearances for the 20-time English champions.
The stopper also made 17 appearances during the 2019-20 season but was not used in 2020-21, having fallen behind Henderson in the pecking order at the club.
Newcastle United's Karl Darlow is also thought to be a target for Man United, with the 31-year-old number two to Martin Dubravka last term, and the Magpies have signed Nick Pope this summer, which will further restrict his appearances for Eddie Howe's side.
Meanwhile, Daniel Bachmann is also believed to be under consideration, with the Watford goalkeeper recently claiming that Man United had been in touch to discuss a possible deal.
"There has been contact with Manchester United. It hasn't just fallen out of the sky... several clubs have shown interest in me - but the most intensive contacts have come from Manchester. It is a massive honour for a club like that to be interested in you," the 27-year-old told Sky Sports Austria.
"I would be second choice behind David de Gea, who has been one of the Premier League's best keepers for years. But anything can happen in football. The performance principle applies. As a result, even big stars can sit on the subs' bench."
Bachmann has played 41 times for Watford in all competitions, including 12 Premier League outings last term, but he could leave following their relegation to the Championship.