Former Germany winger Basler, who won Bundesliga titles with Bayern in 1996-97 and 1998-99 during his playing days, caused a stir over the weekend when he told Sport1 that Ancelotti was bound for the CSL during the next mid-season break, having signed a pre-contract agreement.
The 54-year-old, who spent 10 years of his playing career at Bayern, went onto state that Lewandowski was unhappy with pre-season, but reminded the Poland worldwide that his "dream" club spent 24 days travelling in hot weather.
The 29-year-old said: "Bayern will have to come up with something and be creative if the club wants to keep bringing world-class players to Munich. And if you want to keep up at the very highest level, you need these players" quality'. "In global football that has long since been more of an average [price] than a top price", he said.
Speaking to tabloid BILD on Monday, Rummenigge responded with a warning that any criticism of the club would be considered a criticism of him personally.
Bayern Munich's Robert Lewandowski (right) and coach Carlo Ancelotti during training ahead of the team's Champions League encounter with Anderlecht. On Tuesday, Ancelotti brandished rumours that he was set to leave for China in the winter as "a joke".More news: Egyptian security forces kill 10 suspected militants in Cairo
Despite Lewandowski's fears of Bayern being left behind in the transfer market, Rumenigge said, "We've had a serious and successful philosophy for a long time and enjoyed great success with that".
"I don't think player power is that big", Rummenigge said.
"I'm sceptical about these foreign trips", said Lewandowski.
James Rodriguez's two-year loan from Real Madrid was the only significant bit of business done, along with the arrival of Corentin Tolisso from Lyon for £37.35m, with Lewandowski imploring his employers to do something drastic to attract better players and improve.
Bayern Munich will play host to Anderlecht in the first game of the UEFA Champions League for both sets of teams. I regret his comments.