Having finished fifth at the men's downhill last Thursday at the Winter Olympics in Pyeongchang, Dressen was at Munich's Allianz Arena to see Mueller score twice in the Champions League last-16 first-leg clash on Tuesday.
The Olympics in South Korea close on Sunday, but Dressen is already home in Germany after also finishing 12th in the Super-G and ninth in the combined.
The Bayern fan, who comes from the Bavarian ski resort of Garmisch-Partenkirchen, presented Mueller with his Super-G racing bib from last month's World Cup race in Kitzbuehel.
"It was fantastic night, Bayern left themselves in a great position," said Dressen, with Besiktas facing a near impossible task in the return leg on March 14 in Istanbul.
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"I am a big fan of Mueller, as a person and a player, if he ever wants to go skiing, I'd glady take him along."
Dressen, 24, shot to fame last month when he won the men's World Cup downhill on Kitzbuehel's iconic Hahnenkamm course, the day after the Super-G race.
He was happy to let Mueller, 28, have his World Cup Super-G bib from Kitzbuehel, when he finished 15th, but was not parting with his victorious downhill vest.
"If I put this on now, there will be no stopping me on the slopes," he joked.
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