Upamecano attracted attention from a number of top clubs with his performances for RB Leipzig during the 2019-20 season.
The Frenchman played a key role in Leipzig's run to the Champions League semi-finals, and was rewarded with a contract extension in August, which ties him to Red Bull Arena until 2023.
However, the German club's current head coach, Julian Nagelsmann, has admitted that Upamecano could move onto pastures new next summer.
"Lots of clubs will want to buy - next season it could be real that he leaves the club. But this season he will stay," the Leipzig boss said last month.
Upamecano blew his latest audition on the European stage though, producing an uncharacteristically poor display against United at Old Trafford in a group stage clash on Wednesday.
Marcus Rashford scored three goals as the Red Devils ran out 5-0 winners, with the Leipzig star unable to get to grips with the England international after his introduction as a second-half substitute.
Ex-United centre-half Ferdinand didn't hold back in his criticism of Upamecano post-match, telling BT Sport: "[Rashford] He was head and shoulders above Leipzig.
"He made some defenders, who we were raving about before the game, look like schoolboys. I thought Upamecano had a nightmare today."
Thompson has hit back at Ferdinand's comments by suggesting he is often too quick to judge, while pointing to his ill-timed calls for United to make Solskjaer their new permanent manager following a last 16 Champions League win against Paris Saint-Germain in 2018-19.
The Liverpool great told Paddy Power of Upamecano's "off day" against the Red Devils: “I’ve seen he’s been linked with Liverpool as well as Man Utd now, and of course, after their result, you’d be wondering whether it’s the right call.
"Though on saying that, you could say the same thing about Virgil van Dijk if you had only ever seen him play in that game [7-2 loss] against Aston Villa.
"You have your off days – everyone does. RB Leipzig have had a fantastic start to their season, they didn’t look like that in the second half at Old Trafford, United were all over them.
"Upamecano was all over the place, but so was the entire team. But don’t be fooled. He’s a very good defender and there’ll be a lot of people looking at him because he is making a lot of waves.
"There’s not a lot of quality centre-backs available in Europe at the moment, and I know Rio Ferdinand wasn’t happy with his performance… But I think I remember Rio having one or two bad games himself!
"One or two shockers, it happens to everybody. He’s had a couple of shockers as a pundit, too, we’ve all seen the ‘give it to Ole!’ rant a million times.”