Spurs chairman Daniel Levy is reported to have spoken to the 56-year-old – who guided the Italians to the final of Euro 2012 – following the sacking of Andre Villas-Boas in December.
Levy is also understood to have approached Netherlands manager Louis Van Gaal and Ajax boss Frank de Boer, before offering Tim Sherwood an 18-month contract.
Despite guiding Tottenham to within three points of the top four following six wins from their last eight Premier League matches, Sherwood could still find himself replaced at the end of the season should the club fail to qualify for the Champions League.
Prandelli would be considered a leading contender to take the vacant managerial post, and has reportedly been taking English lessons since Levy’s approach.
Reports in Italy suggest the former Fiorentina and Roma manager would welcome the opportunity to manage in the Premier League.
He also enjoys a close relationship with Tottenham’s technical director Franco Baldini.
Prandelli is expected to hold talks over his future next month, but has already indicated he would like a return to club management.