On their first season in Germany's top flight, RB Leipzig finished second to Bayern Munich in 2016/17 and have qualified directly for the Champions League, but are eager to keep their playmaker Keita.
The 22-year-old has three years left on his Leipzig contract, although Liverpool's manager Jurgen Klopp is eager to lure him to Merseyside.
However Mateschitz, 73, the co-founder of energy drinks firm Red Bull, which backs RB Leipzig, says the defensive midfielder is not for sale.
"We were flattered when an offer of 75 million euros offer for Naby Keita recently landed at our door. No way! He still has a contract and he will fulfil it," Mateschitz told magazine Sport Bild.
Mateschitz says selling Keita would send the wrong message to RB's other stars.
RB Leipzig's Germany striker Timo Werner has been linked to Real Madrid, while Swedish midfielder Emil Forsberg is reportedly being chased by Liverpool and Arsenal.
"To sell him (Keita) would not only be a sign of distrust for our fans, but would also send out the wrong signal to our other players, such as Timo Werner, who are also in demand," added Mateschitz.
Leipzig will not sell talented players to boost their coffers.
"We are not, and will never be, Manchester City," added Mateschitz.
"I have not only the responsibility for the fans from Leipzig but also for the path which we have taken so far.
"We'll do it our way or not at all."