The Polish international has been strongly linked with a switch to the Premier League, with the Red Devils believed to be leading the chase.
With his contract set to expire in 2014, a move sooner rather than later appears to be on the cards, with the German outfit aware that they could lose him for free.
United are thought to be lining up a summer raid for the 24-year-old, but Klopp hasn’t given up hope of keeping the striker at the club:
“We will offer Robert a good contract but we have to see what the players wants,” he is quoted by talkSPORT.
“We must respect the decision of the player and, in some cases, wait.
“Right now there are signs that suggest we may be heading for a divorce but we will see what we can do.”
United chief Sir Alex Ferguson is hopeful that successful negotiations for Shinji Kagawa, who moved to Old Trafford from Dortmund last summer, may aid his pursuit of Lewandowski.
Despite having the likes of Robin van Persie, Wayne Rooney, Javier Hernandez and Danny Welbeck available to him as centre-forward options, the Scot is thought to be keen to add the former Lech Poznan man to his armoury.