The Blues owner believes that the Spaniard needs to make only small changes to his squad and claims that two firm enquiries have been made.
"There is no concern at all, not in the slightest," Sky Sports News quotes Kenwright as saying.
"He has been away and you will always find July 1 onwards - when the current contracts end - is when it will start.
"We have two enquiries going on for two players and if [Martinez] has any concern I haven't felt once ounce of it. He is back at the weekend raring to go."
Martinez, who is currently in the USA working as a TV pundit, is yet to meet the Everton players and assess his squad.
"He hasn't met the squad yet. It is difficult for me talking for Roberto but he thinks the squad is fantastic," Kenwright added. "He wants to hold on to it but he also wants to bring in two or three players in the positions where we need them.
"The first step is to get the players back and get to know them and bring in two or three.
"His absolute passion is youth and he wants to get those players who are there or thereabouts in the Under-21s moving forward to play for the first team."
Everton kick off their new Premier League campaign away to Norwich City on August 17.