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.