Coleman, Barry and Jagielka are all currently nursing injuries, but Martinez believes that the trio could all return before the end of the campaign.
The injury news that Martinez delivered at his press conference was not all good, as he also stated that Gerard Deulofeu would be out for the duration of the campaign.
“We had no knocks or any problems against Bournemouth,” the Spanish boss said. “The three players we are keeping a close eye on are Seamus Coleman, Gareth Barry and Phil Jagielka.
“It will be difficult to see Gerard Deulofeu in any of the three games we have left.
“We are very confident that Jagielka will be available before the end of the season and Barry and Coleman have an outside chance of being involved at the weekend.”
Everton are set to take on Leicester City at the weekend, in what should be a celebration for the new Premier League champions.
Leicester wrapped up the title after Tottenham Hotspur could only draw 2-2 with Chelsea on Monday night.
It is the first time that Leicester have played since securing the title, and there should be an electric atmosphere at the King Power Stadium.
There will be pressure on Everton to pick up a result in the fixture, as Martinez looks to keep hold of his job.
Martinez is under serious pressure, and he cannot afford too many more losses if he wants to remain in charge at Everton.