Furthermore, he is not concerned over a lack of activity in the transfer market so far.
While near-neighbours Liverpool have already tied up four deals, the Toffees have yet to make a move, although enquiries have gone in for two players.
Kenwright feels the real business will start once Martinez - currently in the United States working as a television pundit for the Confederations Cup - returns this weekend ahead of the transfer window officially opening on Monday.
"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."
The Blues chairman said pivotal for Martinez is holding on to the players he has already and supplementing them with a couple of new arrivals, while seeking to promote from within 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," he 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."
The promising talent in Everton's academy may get the boost they need from future participation in the NextGen series, the Champions League equivalent for under-19 sides.
"The previous regime (former manager David Moyes) didn't want to do it," Kenwright told the meeting.
Chief executive Robert Elstone said that stance had now changed.
"I have given Alan Irvine (Everton's academy chief) the blessing and funding which goes with it to go into it," he said.
Areas relating to the club's financial performance during that time was the main topic of debate, but other issues such as the search for a new stadium and Everton's youth development were also covered.
Elstone told the meeting debt levels had remained relatively stable - around the £45million mark - and the club always strived to squeeze the most out of every available resource and opportunity in order to keep pace with bigger-spending sides.
Elstone told the meeting Everton's 'critical success factor' was to "consistently outperform our rivals in recruitment, preparation and training".
"Our singular objective is to be a regular contender for European football," he said.
Delivering a new stadium - as extending Goodison Park "remains insurmountable" according to Elstone - required significant investment from a third party, which meant either new owners or through another funding partnership.
Kenwright said a groundshare with Liverpool, who have shunned a new-build in Stanley Park in favour of redeveloping Anfield, was still on his agenda but admitted it was "not moving forward".
Instead the club are looking, with the help of Liverpool City Council, to find land within the city limits to build their own ground.
"We've had strenuous meetings with (mayor) Joe Anderson from the council," he said.
"The last time we spoke there were six or seven sites, now there are two or three and there is one close to Goodison Park I would love but it is down to the funding package."