As reported by Media Foot, the Red Devils have joined the race to sign the 25-year-old, and are competing with AC Milan and OGC Nice for his signature.
The report also claims that Thuram faces an uncertain future at the Bundesliga club as he only has a year left on his contract. This has prompted Manchester United to think about signing the Frenchman as they appreciate his profile.
Thuram, who is the son of 1998 World Cup winner Lillian, endured an incredibly disappointing last campaign as he scored just three times in 23 appearances.
But the towering striker has scored five times and provided two assists in his three matches so far this season, which has helped fuel speculation about a move in the near future. He has also earned four senior French caps, but failed to score for his nation.
His versatility and ability to play anywhere across the front three will be incredibly useful for any side, as well as his outstanding physical traits and pace.
Manchester United are desperate to sign a new striker this summer, with Cristiano Ronaldo reportedly keen to leave and Edinson Cavani already departed.
Pundit slams 'awful' recruitment at Manchester United over recent years
The 20-time English champions currently sit bottom of the bottom of the Premier League table following a disastrous start to the Erik ten Hag era.
The club have only signed three players this summer following years worth of dreadful additions to the squad. Former Premier League winner Chris Sutton has heavily criticized the Old Trafford hierarchy for their recruitment, as he told BBC Sport:
"I don't think it can get any worse, they have hit rock bottom. The club needs to lower the expectation, if you look at the last decade they have never really challenged.
"They have been miles off for the best part of a decade, if you look at the recruitment over that time can you name one player that has been a massive success that United have brought in? The recruitment has been awful."
Former United captain Gary Neville has also criticized their recent recruitment, as he told Sky Sports (as quoted by the already referenced BBC Sport article):
"It has become a graveyard for players, where players are even considering not coming in. He [Ten Hag] is obviously a fantastic coach but he has been dealt a really bad hand. To not get the players he wanted in is an absolute shocker."