The Blues currently have veteran 'keeper Tim Howard as number one at Goodison Park, with Spaniard Joel Robles providing back up to the American.
However, Howard endured a poor league campaign last year after his exploits with the USA at the World Cup the previous summer, with many calling for him to replaced sooner rather than later.
Martinez though ignored those calls and has seemingly ruled out a move for another goalkeeper while praising the ones he already has.
“In goal we are strong,” he said.
“Joel Robles showed this season that he is a 'keeper with a lot of potential and we are privileged to have Tim Howard.”
The news will come as a surprising one to Everton fans given Howard’s poor season in general, although he did pick up towards the latter end of the campaign.
At 36-years-old though, it’s fair to say the American doesn’t have many more seasons ahead of him in the Premier League, despite the longevity of goalkeepers these days.
The vote of confidence is even more baffling given the fact Martinez was reportedly keen to sign a new long-term keeper back in January, with Cardiff stopper David Marshall being linked with a move by the Daily Mail.