"Our door remains closed, the top quality we have at Bayern Munich will stay here," Rummenigge told Wednesday's edition of Munich-based newspaper TZ.
The UK media has suggested Lewandowski, under contract at Bayern until 2021, could move to Chelsea and the Polish striker's agent revealed in May that his client wants to leave Munich after four successful years.
In the past, Lewandowski has frequently been linked to Spanish giants Real Madrid.
However Rummenigge says Lewandowski, the Bundesliga's top-scorer last season with 29 goals and who has a market value of around 85 million euros ($99 million), is going nowhere -- whatever the amount offered.
"With Robert, we clearly want to send a signal to people within and outside the club: Bayern Munich are completely different to other clubs who get weak when certain sums are mentioned," added Rummenigge.
"We are completely satisfied with him, and in his position there are only a few players who are comparable.
"So it's not in our interest to hand him over - no matter if someone puts 100 or 150 million (euros) on the table."
Bayern have just returned from a two-match tour of the USA, losing 2-0 to Juventus and 3-2 to Manchester City without Lewandowski and their international stars, who were rested after the World Cup.
Rummenigge has ruled out Bayern signing defender Benjamin Pavard, a World Cup winner with France, from VfB Stuttgart this summer.
"No, we have enough quality (at centre-back)," Rummenigge told magazine Sport Bild.
However, several top Bayern players are the subject of rumoured high-profile transfers.
Jerome Boateng is reportedly on the verge of joining Paris Saint-Germain, while Arturo Vidal has been linked to Inter Milan, Thiago Alcantara could return to Barcelona and defender Juan Bernat is up for sale.
At the other end of the financial scale, Bayern have signed Robert Kovac as assistant coach for a nominal fee of just one euro.
Robert, 44, the younger brother of Bayern's new head coach Niko, 46, has joined his sibling in Munich.
The brothers worked together at Eintracht Frankfurt last season and Bayern paid a token amount to buy Robert out of his Frankfurt contract.
"Yes, it's true," Eintracht's director of sport Fredi Bobic confirmed in German daily Bild.
"It could have also been zero, so we agreed on a symbolic gesture of a euro, also for legal reasons.
"It's normal practice, even if it sounds funny."
Bayern start their week-long pre-season training camp in the idyllic Bavarian resort of Tegernsee on Thursday.
They will attempt to win a seventh straight German league title with the new season to kick off on August 24 when they host Hoffenheim. Bayern face Manchester United in their final pre-season friendly on Sunday.