They beat Wolves 2-1 at Molineux, with a late winner from Michael Keane giving them the three points. Alex Iwobi's early opener in that game was canceled out by Ruben Neves' instant equalizer for Wolves.
However, Everton have also progressed to the fifth round of the FA Cup since, putting in a strong showing to brush aside Sheffield Wednesday.
They won that game 3-0 with goals from Dominic Calvert-Lewin, Richarlison and Yerry Mina.
Everton are currently sixth in the Premier League, with 32 points from 17 games. They are eight points behind leaders Manchester United, but with two games in hand.
The Toffees are also six points behind Wednesday's opponents, who have built up a tremendous head of steam.
Leicester City were excellent in their last Premier League game, a 2-0 win over Chelsea, in a match that they dominated from start to finish. That game eventually proved to be Frank Lampard's last league game in charge of the Blues.
The Foxes are currently third in the league, just two points behind United. Like Everton, they also beat Championship opposition in the FA Cup, defeating Brentford 3-1 in a come-from-behind win.
Everton vs Leicester City Head-to-Head
Leicester City have won 38 and lost 44 games against Everton in the past. In total, 32 of the 114 games between these two teams so far have ended in draws.
Everton beat Leicester 2-0 in the league last month at the King Power Stadium, with goals from Richarlison and Mason Holgate.
Everton form guide: W-W-W-L-W
Leicester City form guide: W-W-W-W-W
Everton vs Leicester City Team News
Allan, Fabian Delph and Jean-Phillippe Gbamin will not play this game for Everton. However, both Lucas Digne and Alex Iwobi are available for selection for Carlo Ancelotti's side.
Injured: Allan, Fabian Delph, Jean-Phillippe Gbamin
Meanwhile, Leicester City will be without Jamie Vardy for at least the next two games, as he recovers from a minor hernia operation. Kelechi Iheanacho is likely to take Vardy's place up front.
Brendan Rodgers will also be without Belgian midfielder Dennis Praet. Meanwhile, French midfielder Nampalys Mendy may also be unavailable.
Injured: Dennis Praet, Jamie Vardy
Doubtful: Nampalys Mendy
Everton vs Leicester City Predicted XI
Brentford Predicted XI (4-3-3): Jordan Pickford; Mason Holgate, Yerry Mina, Michael Keane, Lucas Digne; Abdoulaye Doucoure, Andre Gomes; Alex Iwobi, James Rodriguez, Richarlison; Dominic Calvert-Lewin
Leicester City Predicted XI (4-2-3-1): Kasper Schmeichel; Timothy Castagne, Wesley Fofana, Jonny Evans, James Justin; Wilfred Ndidi, Youri Tielemans; Marc Albrighton, James Maddison, Harvey Barnes; Kelechi Iheanacho
Everton vs Leicester City Prediction
Everton have their task cut out against Leicester on Wedneday night. However, without Vardy, it will be interesting to see how Rodgers approaches this game.
Despite the prolific striker's absence, we fancy Leicester to win this game, with the likes of Maddison, Barnes and Tielemans in excellent form.
Prediction: Everton 0-1 Leicester City