Martinez hopeful over trio
Belgian pair Lukaku and Mirallas were absent for Everton's final pre-season friendly against Paderborn on Saturday having only returned to training last week following their World Cup exploits.
Coleman, meanwhile, has been nursing a hamstring injury since limping out of the club's 2-2 draw with Tranmere Rovers last month.
Martinez says all three have now returned to training, but could not confirm whether they would be involved in Everton's Premier League curtain-raiser against Leicester City this weekend.
"All three are going to train normally with the team today, so we need to assess how they are and how they go through the week before any decisions are made on Saturday," he told the club's official website.
"It's really good to see Rom and Kevin reaching a really good level of fitness so quickly, but we don't know yet if they're going to be ready for the weekend.
"Seamus is training with the team and had the 'all okay' from a scan yesterday, so that's very good news as well."
Martinez is also confident over the recovery of long-term absentee Arouna Kone - out since October with a knee problem.
"Arouna is training well and is still in his own programme but he has been working with the team as well," he added. "We're very positive about Arouna being able to play some sort of competitive football in the next four to five weeks."