Heaton began his playing career at Old Trafford but departed the club permanently in 2010 for Cardiff without making a senior appearance.
The England international made his name at Burnley before joining Villa in 2019, where his progress was disrupted by a cruciate ligament injury last season.
According to the Telegraph, United are closing in on a deal to bring Heaton back to Old Trafford on a free transfer this summer, when his contract at Villa Park expires.
The Red Devils hierarchy are on the hunt for a reliable back-up to Dean Henderson and David de Gea, who have battled for the No.1 shirt this season.
Argentina international Romero is set to depart at the end of his contract in June and a reunion with Mourinho could be on the cards in Rome.
The 34-year-old has an Italian passport and Roma are one of several Serie A clubs to express interest.
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