The Toffees are yet to make a signing since the appointment of Martinez, while near neighbours Liverpool have already tied up deals for four new recruits.
Kenwright is not worried by Everton's lack of activity, insisting the club have made two enquiries, and expects Martinez to secure moves when he returns from the United States where he is working as a television pundit.
"There is no concern at all, not in the slightest," said the chairman, speaking after the club's first Annual General Meeting in five years.
"He has been away and you will always find July 1 onwards - when the current contracts end - is when it will start.
"Liverpool have had a sale (Andy Carroll to West Ham) in the transfer market, have got some money in and are spending some money.
"We have two enquiries going on for two players and if he (Martinez) has any concern I haven't felt once ounce of it.
"He is back at the weekend raring to go."
Kenwright admits that Martinez's top priority is keeping the club big-names, but he does expect a few new arrivals and more players being promoted from the youth system.
"He hasn't met the squad yet. It is difficult for me talking for Roberto but he thinks the squad is fantastic," said Kenwright.
"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."
Chief executive Robert Elstone Elstone told the meeting that debt levels remained around the £45million mark, but the club's hierarchy expect to compete in the top half again next season.
"Our singular objective is to be a regular contender for European football,"