Sanchez, 28, recently said that his future is "clear" and is expected to leave The Emirates Stadium this summer, with Manchester City hopeful of completing a £50m deal for the former Udinese wonderkid.
Bayern Munich were believed to be in the hunt to sign Arsenal's talisman - Carlo Ancelotti spoke of his admiration for his Sanchez late last week - but Hoeness seemed to balk at the thought of bowing to Sanchez's astronomical wage demands and revealed that chairman Karl-Heinz Rummenigge has not discussed the possibility of signing the former Barcelona star with him.
"I'm not in the operational side. [Chairman] Karl-Heinz Rummenigge has not yet come to me, so the matter doesn't seem to be too urgent with him," Hoeness was quoted as saying by Sportskeeda. "A €20million salary is probably not feasible."
Arsenal are still hoping they can convince Sanchez that his future lies at the Emirates and tie him down to a new long-term contract. Arsene Wenger's side are poised to wrap up the signing of long-term target Alexandre Lacazette, who is expected to be announced by the Gunners within the next 24 hours.
Wenger hopes the Lyon forward will complement Sanchez rather than replace him, but the Frenchman has an awful lot of work to do in the transfer market with a number of Arsenal stars facing uncertain futures.
On the other hand, Bayern have moved swiftly in the transfer window, completing most, if not all of their business before the start of July. Sebastian Rudy, Niklas Sule, Serge Gnabry and Corentin Tolisso have all arrived at the Allianz Arena, but Brazil international Douglas Costa may be leaving Carlo Ancelotti's side with Juventus reportedly keen on bringing him to Turin.
Bayern signed Costa for £25m in the summer of 2015, and Hoeness was keen to stress the former Shakhtar Donetsk attacker will not leave Germany unless Rummenigge's demands are met.
"As long as he has not signed anywhere else, he'll return, and if the signing does not happen then he will start the season on August 18," Hoeness added. "When a club comes and pays the sum that Karl-Heinz Rummenigge has asked for, he will leave. We paid a lot of money so we want to get more."