The 64-year-old coach has led unsung Leicester, 5 000-1 outsiders at the start of the campaign, to the Premier League title this season, the first top-flight crown in the club's 132-year history.
“I hope Ranieri can win a World Cup with Italy, that would be the best,” Tavecchio told reporters.
“I'm speaking in an abstract way, of course, and not necessarily about the next World Cup (in 2018). Claudio is still young and will have time on his side.”
Italy will be coached by Antonio Conte at next month's European Championship in France before the former Juventus supremo leaves to take charge of Chelsea, Ranieri's old club.
“Have we thought about him (Ranieri) as a replacement for Conte?” said Tavecchio.
“It's him who should be thinking about us.
“We're thinking about a lot of different things right now but those in his second sporting homeland are wishing him every success.”
Earlier on Monday, Ranieri was honoured as Italian football's coach of the season.
Two days after lifting the league title, he was back in his home city of Rome to collect the Enzo Bearzot award, named in honour of Italy's late 1982 World Cup-winning coach.
Ranieri also received the Palma d'Oro (Golden Palm), the top honour the Italian Olympic Committee can bestow on any coach. – Reuters
Original source: Ranieri could lead Italy to WC glory