Bayern have one foot in the quarter-finals with Besiktas facing a near impossible task for the return leg in Istanbul on March 14.
Both Mueller and Poland striker Robert Lewandowski scored twice as Bayern ran riot in the second half in Germany.
"Everything is possible," Mueller said when asked whether Bayern can repeat their 2013 haul of Champions League, Bundesliga and German Cup titles.
However head coach Jupp Heynckes, 72, who oversaw the treble five years ago, insists Bayern must do better if they want all three titles again.
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"Everyone in the stadium saw that we found it hard in the first half.
"We didn't find our rhythm and we were nervous -- I don't know my team like that.
"In the first half there wasn't any tempo to our game, our passing was off and it allowed Besiktas to attack us more.
"The opener before the break gave us a psychological advantage and in the second half we saw a different Bayern team.
"We scored some great goals and played some good football."
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Disaster struck for Besiktas after just 16 minutes at the Allianz Arena when Croatian defender Domagoj Vida was sent off for hauling down Lewandowski as he was through on goal.
Mueller broke the deadlock just before half-time when he scored his first from close range.
The floodgates then opened after the break as Kingsley Coman struck before Mueller poached his second.
Lewandowski then scored two late goals to leave him with 29 goals in all competitions this season, as Bayern -- 19 points clear in the league and through to the German Cup semi-finals -- claimed their 14th straight victory.
"It's been five years since all our outfield players were fit and the trainer doesn't have it easy, but everyone who came on did a good job," said Mueller.
"Arjen made us a bit more aggressive, Franck also did well and we need that extra bit of power from the bench."
Robben came on when James Rodriguez limped off with a calf injury on 44 minutes.
The Dutchman was heavily involved in Mueller and Lewandowski's second goals, but was unhappy at being left out of the starting side.
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"Of course, I was disappointed, but I don't want to say any more because if I speak my mind, I will end up in front of 'Brazzo' (Bayern's director of sport Hasan Salihamidizic)," said Robben.
Like Ribery, Robben, who scored Bayern's winning goal in the 2013 Champions League final is out of contract in June.
However, Heynckes sees it as a positive to have so much experience on Bayern's bench.
"I am very pleased to have a squad like this in case of injuries and illness in the future," he said.
"Any top player like Arjen Robben wants to play from the start, but we have so many good players.
Besiktas were making their debut in the knock-out stages of the Champions League and their head coach Senol Gunes said his side learned a harsh lesson.
"We won or drew all our games in the group phase, but tonight the opponent was better," he said glumly.
"After the sending off, it became too difficult for us.
"We suffered mentally and physically, they took advantage."
Gunes swapped striker Vagner Love for defender Dusko Tosic in the second half, but it made little difference.
"We tried to limit the damage and focus on the second half, but we couldn't manage it," said the Besiktas boss.