Leicester are priced at (4.13) for the win, with the draw at (3.74) and Spurs are at (1.85) to claim an away win.
Shakespeare's side come on the back of a 2-1 defeat to Manchester City, to extend their poor away form. The club are only two points behind tenth-placed Bournemouth.
The Foxes lost at Man City last weekend, but their home form remains quite strong and could surprise the host in this tie.
Tottenham are undefeated in their last three visits to the King Power stadium, and Leicester have managed just two wins in the last eight matches of all competitions.
However, the Foxes have won their last three home games with a clean sheet too.
Spurs have failed to score in three out of the last six away games, but have scored nine goals in their last five games and two goals in their last games on the road against Leicester City.
Leicester City have scored over 1.5 goals just twice in the last eight games across all competitions. Only one of the last five meetings between the two teams has produced over 2.5 goals.
A win for Leicester City in this tie will make it six wins out of six at home under Craig Shakespeare, before finishing off their campaign at home to Bournemouth on Sunday.
In the anytime goalscorer market, Jamie Vardy is a price of (3.00), and he has scored in two of his last three league home matches.
Only once in 10 previous home matches against Tottenham in the Premier League have the Foxes failed to score.
Since the beginning of September, Harry Kane has scored 22 goals in 25 Premier League appearances for Tottenham Hotspur.