Tavecchio allegedly made the comments during an interview for the online football magazine, Soccer Life, in June, with a recording published on the Corriere della Sera website on Sunday.
The alleged remarks were made while Tavecchio was talking about the sale of an amateur league's headquarters to a Jewish-Italian property investor, Cesere Anticoli.
“It was bought by that Jew, Anticoli,” Tavecchio can be heard saying.
“It's best to watch them carefully,” he adds, in reference to Jewish people.
Tavecchio can then be heard making homophobic comments.
“I don't have anything against gays – but keep them away from me,” he says.
When challenged about the remarks by Corriere della Sera, Tavecchio told the paper that he didn't remember making them and suggested the recording “might have been manipulated”.
He also claimed he was being blackmailed by the magazine's editor, because “I didn't give him funding which he wanted”.
But the 72-year-old politician, who was elected president of the Italian Football Federation in August 2014, has a long history of making offensive comments.
During his election campaign, he courted controversy by making a racial slur while talking about youth football in Italy – when he referred to a fictional player called 'Opti Pogba', who “previously ate bananas but now plays first team football with Lazio”.
Tavecchio was elected in spite of his comments, but received a six-month ban from Uefa in the wake of the incident.
Just days after making the racial slur, Tavecchio found himself in trouble again for saying all women were “physically handicapped” when it came to sport.