Lewandowski's present Dortmund contract runs until the summer of 2014, but the Bundesliga champions are keen to ward off interest from Manchester United in their star striker by extending his current deal.
TalkSPORT claim Lewandowski is expected to move to Old Trafford at the end of the season, but Dortmund coach Jurgen Klopp has revealed the club plans to offer Lewandowski an improved contract to try and convince him to stay.
"We will offer Robert a good contract but we have to see what the player wants," said Klopp.
"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."
Sir Alex Ferguson has a stable of top strikers at Old Trafford already, although the prospect of a Robin Van Persie-Robert Lewandowski partnership would excite most Manchester United fans.
Wayne Rooney, Javier Hernandez and Danny Welbeck are all competing for a starting place as well, giving the Premier League leaders plenty of options going forward. Ferguson's sit currently sit top of the Premier League table, seven points clear of last year's winners Manchester City.