Whelan told the BBC that he had tied up a deal as Everton seek a successor to David Moyes.
"Bill Kenwright (Everton chairman) and myself have agreed a deal," he said.
Everton have not confirmed the identity of the man they want to replace Moyes after he departed for Manchester United.
And they refuted Whelan's claim through a statement on their official website.
"Everton statement on the managerial position: in response to regrettable and somewhat premature reports earlier this evening, Everton Football Club are continuing discussions with regards to the vacant managerial position," it read.
"Whilst positive moves are being made, the club will officially announce details as and only when they are agreed and completed."
Martinez asked to leave Wigan last week having guided the club to FA Cup glory before being relegated from the Premier League.
Everton lost Moyes to champions United after Alex Ferguson's retirement last month.