The 18-year-old has attracted significant attention after making an impressive breakthrough at Bayern, but recent public comments from honorary president Uli Hoeness have prompted discussion about his position at the German club.
Hoeness recently said he intended to have a serious conversation with Karl, adding that the youngster appeared to believe he was already a superstar.
“He thinks he is already a superstar, but he is not,” Hoeness told Die Welt am Sonntag.
“Young players need humility. Young players also need pressure. I don't know whether it is good for Lennart Karl that he is constantly being overprotected.”
According to Bild, the comments have alerted several Premier League clubs, with Arsenal, Liverpool and Manchester United making contact to establish the situation surrounding the Bayern Munich youngster.
The enquiries do not amount to formal offers, but they indicate that the three English sides are monitoring developments at the Allianz Arena.
Bild transfer journalist Christian Falk has suggested Bayern could be open to discussions, although the club are not looking to push Karl towards the exit.
“His transfer value is €60 million. Of course, every Premier League club can easily afford that,” Falk said.
He also confirmed that Bayern have yet to hold talks with Karl over a new contract. The teenager's current agreement runs until the summer of 2029.
Despite the speculation, Falk stressed that Bayern do not intend to sell their highly rated prospect cheaply.
“They certainly don't intend to do that. They won't sell him for a pittance,” he added.
Karl has already made 51 competitive appearances for Bayern, establishing himself as one of the most exciting young players to emerge from the club's academy in recent years.
He made history in the Champions League last season, becoming Bayern's youngest goalscorer in the competition at the age of 17 years and 242 days.
The interest from England comes at a sensitive moment for Karl, but there is no indication that Bayern are actively seeking a transfer. The club's position remains that the teenager is an important part of their future, even as senior figures expect him to maintain perspective as his profile grows.