Italy have been without a coach since Giampiero Ventura was sacked after the four-time champions failed to qualify for the World Cup finals last November.
Tavecchio was forced to resign as FIGC chief but will remain in charge until his successor is elected later this month.
“I’m in charge until January 29th, and I don’t think that by that date there will be the new national team coach,” the 74-year-old said on the sidelines of the presentation of the new 2017-2018 Panini Collection in Milan.
“I won’t be the one that chooses the new coach. I can also tell you that the best coaches are under contract until June. It’s difficult for the new coach to be appointed before then.”
Among the names being touted are Zenit Saint-Petersburg’s Roberto Mancini, Chelsea manager Antonio Conte and former Bayern Munich coach Carlo Ancelotti.