Goal.com understands the newly crown Bundesliga champions are leading the chase for Lewandowski ahead of United, who have made the Poland international a priority summer signing.
Lewandowski scored four goals against Real Madrid in the Champions League on Wednesday and has been the subject of intense speculation over recent weeks as the new Bundesliga champions were rumoured to have secured his services.
|MANCHESTER UNITED LATEST
|5/1||Man Utd are 5/1 with Bet365 to score over 2.5 goals against Arsenal
"If the right player comes along you have to be prepared to make a move, I can find room for anybody here as long as they have the required quality," he told reporters.
"I am not sure Lewandowski will be sold to Bayern now. The Dortmund fans are not going to be happy and I don't think they will sell to their main rivals. I think they will either let his contract run out, or sell him somewhere else."
The veteran manager spoke of Dortmund's fortunes in the Champions League as he openly admired their team and appeared to eagerly anticipate the prospect of an all-German final.
"But for the referee [in United's defeat to Real Madrid] it would have been us facing Dortmund and we would have had to do a good job, because they are a good side," the Scot observed.
"Our target for next season is to do better in Europe, possibly by adding a player or two, but it will be interesting if this season's final is an all-German affair.
"I have said all along that Dortmund have been prioritising the Champions League this season. They have an unbelievable record against Bayern so, despite what the German league table might say, if the two sides meet in the final it wouldn't be a gimme for Bayern."