Aside from a loan spell at Salernitana in 2015-16, the 27-year-old has spent his entire professional career with Lazio, making 208 appearances for the Italian giants in all competitions.
The 19-time Albania international left the Serie A outfit at the end of June following the expiration of his deal, though, and he is therefore available on a free transfer this summer.
Chelsea have recently been credited with an interest in the goalkeeper, but according to talkSPORT, Man United are now closing in on his signature.
The report claims that the 20-time English champions recently held talks with the stopper's representatives and are confident that an agreement will be reached in the near future.
Man United are in the market for a new goalkeeper this summer, as Dean Henderson has been allowed to join Nottingham Forest on loan for the 2022-23 campaign.
David de Gea is again expected to be the team's number one next term, having impressed during a difficult 2021-22 season for the 20-time English champions.
Tom Heaton is the only current senior back-up to the Spain international, as Lee Grant retired from football earlier this summer.
There are currently four goalkeepers with the Man United squad in Thailand preparing for their opening friendly of the summer against Liverpool on July 12, but Nathan Bishop and Matej Kovar are both likely to leave the club on loan before the end of the summer window.
Strakosha was a key player for Lazio between 2017 and 2010, but he only made 11 appearances for the Italian giants during the 2020-21 campaign.
The Albanian also spent the first half of last season out of the side but finished the campaign as the number one goalkeeper for the White and Sky Blues.
Sergio Romero has also been linked with a return to Man United this summer following his release from Venezia, but the club are not believed to be considering moving for the Argentine at this stage.
Watford's Daniel Bachmann and Newcastle United's Karl Darlow are also believed to be on the club's shortlist when it comes to finding a replacement for Henderson.
Man United have only made one signing during this summer's transfer window, bringing in left-back Tyrell Malacia from Feyenoord.
The club are believed to be looking to sign five players before the end of the month, though, with the Red Devils currently short in a number of areas, less than one month before the start of the new Premier League season.