Lewandowski, who scored a stunning four goals in Wednesday night's semi-final first leg against Real Madrid, is out of contract next summer and was expected to decide on his future at the end of this season with Manchester United strongly interested.
On Tuesday Dortmund confirmed Bayern had activated Gotze’s € 37million (Dh176.9m) release clause and Lewandowski looks now to be following his team-mate to the Allianz Arena.
Enrique Reyes, whose client will be replaced by Pep Guardiola on July 1, said: “Bayern have signed Lewandowski. Yes, right now, they have Lewandowski and Gotze. The problem is that Bayern have a lot of money. They are doing what they did with Javi Martinez.
“If a club don’t want to negotiate with you, what do you do? Why, pay the buy-out clause, of course.”
Lewandowski's agent has since confirmed that his client has received a "very interesting offer" from Bayern, although it appears Dortmund have yet to sanction the sale of another of their top stars to their arch rivals.
Lewandowski has netted 20 goals in his last 18 games - scoring in 12 successive Bundesliga games in the process - establishing himself as one of the best finishers in European football.
If Reyes’ words are to prove true it would further push Mario Gomez towards the exit door at Bayern with German reports earlier this week claiming he had an offer on the table from Premier League Chelsea.
The striker is also understood to be interesting Italian champions Juventus with Antonio Conte and sports director Fabio Paratici in Munich on Tuesday to see Bayern beat Barcelona 4-0. Conte was also scouting Barca winger Alexis Sanchez.
Guardiola’s revamping of a squad that could potentially win a treble continues at some velocity with Bayern also understood to have agreed pre-contract arrangement to sign Eintracht Frankfurt midfielder Sebastian Rode, 22, and Mainz defender Jan Kirchhoff, 22.
Eintracht Frankfurt coach Armin Veh said on Saturday of Rode: “He has informed us that he has other plans for 2014. If that is so, that he can go to Bayern Munich, you have little arguments.”
Watch Lewandowski's four goals against Real Madrid: