The 32-year-old arrived at Frankfurt from Paris Saint-Germain in 2018, initially on loan, and he has represented the German side on 304 occasions in all competitions during two separate spells.
Trapp was again Frankfurt's number one during the 2022-23 campaign, making 48 appearances, keeping 11 clean sheets in the process, and he still has another three years left to run on his contract, having signed an extension earlier this year.
However, according to The Mirror, Man United have identified the Germany international as a genuine target this summer to become their new number one goalkeeper.
The report claims that Red Devils head coach Erik ten Hag is determined to bring in a new stopper, and Trapp is seen as a cheaper alternative to Inter Milan's Andre Onana.
There have been suggestions that Inter would want in excess of £50m for Onana, which is unrealistic this summer, with Man United committing £60m to signing Mason Mount from Chelsea.
The Red Devils are also determined to sign a new centre-forward, although there have been claims that their budget to bring in a new attacker is only £65m unless there are first-team sales.
Feyenoord's Justin Bijlow is also being linked with a move to Old Trafford, and the Netherlands international would allegedly be available for a fee in the region of £20m.
Trapp, though, could reportedly be purchased for around £10m, which would allow Man United to put more money towards signing a centre-forward and potentially a centre-back.
David de Gea's contract at Old Trafford came to an end on Saturday, with the Spaniard officially a free agent, although he could yet return to Man United in the near future.
As it stands, Dean Henderson and Tom Heaton are the only two first-team stoppers at Old Trafford, with the former back at Carrington after a loan spell at Nottingham Forest.
Henderson is widely expected to move to Forest on a permanent basis this summer, though, potentially for a fee in the region of £25m, while Heaton is only seen as a number two or a number three.
Trapp initially represented Frankfurt between 2012 and 2015 before moving to PSG, spending four years with the French giants before securing a permanent return to the Bundesliga side.
The experienced goalkeeper has also been capped on seven occasions by Germany and was a part of their squad at the 2022 World Cup in Qatar.