Bayern, who also won the domestic double last season, enjoyed a record-breaking campaign under former coach Jupp Heynckes, becoming the first German team to win the treble.
The club have spent more than 60 million euros ($79.9 million) on transfers in the close season under new coach Pep Guardiola and will be competing in the European Super Cup and the club World Cup in December in addition this season.
"We want to achieve something that has not been done in Europe before," Sammer told Sport Bild magazine. "We want to go after the treble again and on top of that we want the European Super Cup and the club World Cup."
Bayern have brought in gifted Germany midfielder Mario Goetze from rivals Borussia Dortmund in a 37 million euro deal as well as sought-after Spain Under-21 international Thiago Alcantara from Barcelona.
A deal for Dortmund striker Robert Lewandowski fell through with the Ruhr Valley club blocking the move repeatedly.
Bayern's biggest transfer coup, however, was signing former Barcelona coach Guardiola on a three-year deal.
"We want to become even stronger," Sammer said. "That is why I do not understand any discussions about being satisfied."
He said last season's treble win was in no way damaging motivation.
"It's about pulling up our sleeves and getting to work. Everything starts from scratch. If we do not show ambition and willpower then we are not worthy of working for Bayern," he said.
"Everyone has to ask themselves every day if they bring this willingness with them."
Bayern, who lost 4-2 to Dortmund in the German Super Cup two weeks ago, kicked off their domestic season with a 5-0 win over fourth-tier BSV Rehden in the German Cup first round.
They face Borussia Moenchengladbach in the Bundesliga opener on Friday. ($1 = 0.7513 euros)