The Moroccan international scored both goals against Fulham last weekend to help the R's pick up their first win of the Premier League season.
"I have been told that the president of Anzhi and people from Barcelona have asked about me," the 23-year-old is quoted as saying by The Sun. "But I have just signed a four-year contract with QPR, and the chairman Tony Fernandes has told me that he will not sell me.
"I don't know what would happen if someone offered £20m for me, but I love the club and the fans, and they love me too."
Taarabt moved to Loftus Road from Tottenham Hotspur in 2010.