Levels started 23 league games for Gladbach last season, but is believed to have been told by Lucien Favre that he can look for a new club.
The 24-year-old, who has two years left on his current deal, is now reportedly attracting attention from England.
Levels, who can play full-back or in central defence, revealed that Bolton have been tracking him for some time.
"It was not the first contact with the club [Bolton], they have known about me for some time," he told Kicker. "The Premier League fascinates me and to play there would be a great challenge.
"I have always said that England interests me."