Having picked up just four points since March 5, the Toffees are 12th in the Premier League, and were beaten 3-0 by Sunderland – their fourth loss in their last five matches – to stretch their poor run of form to just one win in 10 matches.
Everton also lost in the semi-finals of the FA Cup and League Cup this season.
The 2015-16 season has been another disappointing campaign for Martinez and Everton, who have won only five times at Goodison Park – only Aston Villa and Bournemouth have conceded more goals at home.
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They have conceded 18 points from winning positions this season, with only one match remaining, they are guaranteed to finish in the bottom half of the Premier League for a second successive year.
Martinez, who had three years remaining on his contract, was appointed as David Moyes’ successor in June 2013 and guided Everton to their best Premier League points tally – 72 – and a fifth-place finish in his first season in charge.
The club are expected to make an official announcement imminently to confirm their decision.