A potential move to the Premier League has also been mooted for Upamecano, with Manchester City, Manchester United and Arsenal all reportedly keeping a close eye on the centre-back.
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France Under-21 international Upamecano has made 76 league appearances for Leipzig since joining from Salzburg in 2017, particularly catching the eye in his 21 outings this season.
Interest in the talented defender may be growing, but Bayern great Matthaus suggests leaving the Red Bull Arena later this year may not be the right choice.
"I can see him playing for all the big club when he gets more experience," Matthaus told Sky Sports in Germany.
"If he does leave, he needs to make sure his new coach or club gives him the confidence to play regularly - as he is doing at Leipzig.
"He's a young player, highly rated, fast, has a good positional game and uses his body well for a 21-year-old. But a year or two in Leipzig would not hurt him.
"Leipzig are a top team - one of the last eight remaining in the Champions League.
"I can still see one or two per cent where he can learn, but he's a huge player and that's why I'm not surprised that top clubs in Europe are after him.
"But you can't speculate much about change because you need to see how the [coronavirus] situation develops."
Upamecano is under contract with Leipzig until the end of the 2020-21 season, and is reportedly valued at around €70 million ($61m).
All potential suitors will have to wait before launching any formal bids for the Frenchman, with the transfer window set to be moved amid the coronavirus pandemic.
The current season has been postponed until such a time it safe for players and staff at clubs across Europe to return to work, but all fixtures could yet be voided completely if the crisis continues through the summer.