Despite speculation linking Everton left-back Leighton Baines with a move to Manchester United, the new Toffees boss has confirmed the English international will be on tour with his side.
Baines will travel with the Everton squad on their tour of the United States after he was missing with a hip injury as his teammates beat Blackburn 3-1 in their latest preseason friendly.
Martinez, who this week said there had been no recent offer for Baines from Manchester United or anyone else, expects the player to be fit to participate across the Atlantic.
"I don't think he's going to be out too long," said the former Wigan manager.
"He's going to travel with the team, so if I thought he didn't have a chance to participate in the games in the USA then it wouldn't be right for him to travel.
"At the moment, bearing in mind he recovers quite quickly, it was just a precaution we took with him (not to play against Blackburn).
"We hope that Leighton can be fully fit very, very soon."
Everton's International Champions Cup campaign begins against Juventus in San Francisco on Wednesday, with further games in Los Angeles and Miami to follow.