Karl-Heinz Rummenigge says Robert Lewandowski could extend his contract with Bayern Munich and has ruled out a deal to bring back Mario Mandzukic.
Poland striker Lewandowski appeared to be agitating for a move away from the Allianz Arena 12 months ago but was unable to secure an exit.
He went on to score 40 goals last season as Bayern won the domestic double and admitted in March he could see out his career at Bayern after becoming much more settled.
Chairman Rummenigge now hopes Lewandowski will agree to a new contract as he believes the 30-year-old could play for several more years. Lewandowski's current deal covers the next two seasons.
"It's not all wrapped up, but there's already the development with Robert that he feels extremely comfortable with Bayern Munich," Rummenigge said to Bild.
"When you look at his body, this is a player who can easily play at this level for a few more years."
Rummenigge also dismissed talk that former Bayern striker Mandzukic could be brought back to the club from Juventus as support for Lewandowski, saying: "Nothing is planned in that direction."
However, Rummenigge did confirm Bayern remain eager to sign another winger to help fill the void left by Arjen Robben and Franck Ribery, who left at the end of last season.
"We still need a winger because we lost two with Franck Ribery and Arjen Robben," said Rummenigge, with Bayern still thought to be interested in Leroy Sane and Ousmane Dembele. "But I don't want to promise anything because there is no point in making big promises."
Rummenigge added he is confident head coach Niko Kovac can make further strides with the club in 2019-20 thanks in part to their impressive strength in depth in defence.
"When I look at our defence, with [David] Alaba, [Lucas] Hernandez, [Niklas] Sule, [Joshua] Kimmich, [Benjamin] Pavard and Jerome [Boateng], where we have to wait and see what's going on with him, I have to say I don't see many better in Europe," he said.
"Also, what we have to offer up front... it's all good. We have a good team and a good squad; the transfer market is not over yet. When the Bundesliga starts, I'm convinced our team will be very focused and motivated to get to work.
"Niko knows we are a club that needs success. We're interested in continuity, in the coaching position as well. I wish him as successful a second season as he had last year, with the double, and perhaps one more round in the Champions League. Everyone would then be very happy with Bayern."