Martinez is the firm favourite to succeed David Moyes after Wigan confirmed they had granted the Merseysiders permission to speak to the Spaniard.
Yet Kenwright insists the 39-year-old is not the only candidate and other options will be explored.
Cardiff's Malky Mackay and Porto coach Vitor Pereira have also been linked with the position while there are also internal candidates in David Weir, Phil Neville, Duncan Ferguson and Alan Stubbs.
Kenwright told Sky Sports News: "I will meet Roberto in the next 48 hours. He is on the list, as I have always said."
Martinez has been courted by Aston Villa and Liverpool in each of the past two summers but remained at the DW Stadium, where he took charge in 2009.
His stock has risen again this year following Latics' stunning success in the FA Cup but he has opted to leave the club after failing to avoid relegation from the Premier League.
Everton are looking for a new manager for the first time in 11 years following Moyes' decision to move to Manchester United.
Kenwright feels he has the support of the majority of fans as he leads the recruitment process.
He said: "The most gratifying thing is 90 per cent have said, 'You didn't let us down last time, go with your gut instinct and hopefully you'll get it right again'.
"All I can say is there is no way that I or anyone can say, 'We'll get it right, we'll get the right man', but I certainly will put everything into getting it right and getting the right DNA for Everton Football Club."
Martinez first came to English football when he joined Wigan as a player in 1995.
He later played for Motherwell, Walsall, Swansea and Chester before beginning his management career back at Swansea.
His successes at Wigan principally involved keeping the club in the top flight against the odds until this year's victorious cup run, which included a quarter-final defeat of Everton.