Current CSO music director Daniel Barenboim will step down at the end of next season.
Muti told the Italian newspaper La Repubblica, "They have asked me to consider their offer. Since we are dealing with one of the most prestigious orchestras in the world, I greatly appreciated their invitation."
More precisely that, however, he would not say, adding, "For now, I don't want to make other statements."
Earlier this month, Muti resigned his post as music director of Milan's Teatro alla Scala after the opera house suffered a series of worker strikes and accusations that Muti was wielding too much influence.
Of the New York Philharmonic, which he recently led in a series of concerts, he said, "New York is a city where I have always worked very well, there is a great understanding with the musicians, and I feel that the public is close to me."
From 2006-07 through 2008-09, Muti will conduct the Philharmonic for four weeks per season. "Then," he said, "we'll see." Current Philharmonic music director Lorin Maazel will retire at the end of 2009-09.
Upcoming events for Muti include a tour that includes concerts with the Vienna Philharmonic, and performances of Mozart's The Magic Flute in Salzburg, which, Muti said, "is the ideal place to think."