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According to reports, Bayern’s director of sport Hasan Salihamidzic has recommended Pochettino to club bosses Karl-Heinz Rummenigge and Uli Hoeness.
Current head coach Heynckes, 72, has implied he will leave at the end of the season and magazine Sport Bild claims Salihamidzic has approached the Spurs boss.
“I know that Bayern have contacted Mauricio Pochettino,” Sky pundit Didier Hamann told the German magazine.
“He was an option and possibly still is.”
Highly-rated Argentinian Pochettino, 46, has a contract at Spurs until 2021 and Tottenham president Daniel Levy is unlikely to let him go after nearly four years.
Bayern had been thought to want to hire a German-speaking coach.
“That doesn’t have to be the case, if we said that we would automatically close a door — and it’s not closed,” Salihamidzic has said on the matter.
Other possible candidates to succeed Heynckes include ex-Borussia Dortmund coach Thomas Tuchel, currently without a club, and RB Leipzig handler Ralph Hasenhuettl.
The Austrian has been offered a contract extension past 2019, but negotiations with Leipzig are currently on ice.
Bayern chairman Rummenigge is also said to admire Nice coach Lucien Favre, who has a buy-out clause in his contract with the French Ligue 1 club.
Swiss coach Favre, who has coached Bundesliga sides Hertha Berlin and Borussia Moenchengladbach, has proven he can work with big name stars, such as Mario Balotelli, who has scored 14 French league goals this season for Nice.
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