The Toffees began their summer preparations on Tuesday, with a 2-2 draw against Tranmere.
Leicester are also one game into pre-season, having racked up a 6-1 win against Ilkeston.
The last time these sides met in competitive terms was 2004, in a 1-1 draw at the Walkers Stadium.
Everton have lost just one of their 16 most recent games with the Foxes, though 11 have ended in a draw.
Everton haven't named their touring party, only stating that Bryan Oviedo and Arouna Kone are still not fit and will remain behind, per the official Everton website.
Roberto Martinez also revealed Seamus Coleman's knock against Tranmere will prevent him from travelling to Thailand, as he told the club's website:
He will miss the Thailand trip to give proper consideration to his injury, for proper treatment and to remove any chance of aggravating that feeling that he had.
We don’t really know the extent of the injury yet but it is sometimes a little bit of a setback that comes with pre-season preparation and getting a lot of volume into the bodies.
Elsewhere, Ross Barkley is in the 22-man squad, though it seems his World Cup team-mates have stayed behind.
Potential new signing Muhamed Besic will also travel to Thailand but won't feature in the game.
With that team news considered, here's a look at Martinez's potential starting XI:
Predicting pre-season line-ups is pure guesswork. It's rarely about deploying the strongest unit but instead involves experimenting with partnerships and blending youth with experience.
Everton have 22 players with them and could again field two different sides. However, stronger opposition and an expectant Thailand may demand a more prominent selection.
The above side would be Martinez's strongest-available XI, assuming Barkley is not yet fit enough to start.
With most of Everton's World Cup players yet to return, Joel Robles would start in goal behind Tony Hibbert, John Stones, Sylvain Distin and Luke Garbutt.
Gareth Barry and James McCarthy would anchor midfield with Steven Pienaar, Aiden McGeady and Leon Osman ahead.
With very few alternative options, Steven Naismith would then continue up front.
It wouldn't be a surprise to see a similar side play for 60 minutes before a deluge of substitutions in the final 30.
Everton kept to the 4-2-3-1 shape they played for most of last season against Tranmere, but don't be surprised to see Martinez switch to a back three at some stage this summer.
Key Points for Martinez
While he won't be overly concerned about the result, Martinez will want to see gradual progression from Tuesday's draw with Tranmere.
He will want to see fewer wasted passes, a quicker overall tempo and some sharper exchanges in the final third.
Martinez will also want to iron out the defensive mistakes that handed Tranmere their goals, and he will want his team to exhibit better all-round resilience.
Prediction: Everton 1-1 Leicester