Full-back Coleman and midfielder Besic both came off in the 3-1 home win over Chelsea last weekend due to hamstring problems.
But speaking on Thursday ahead of the trip to the Liberty Stadium, Martinez said: "We have had positive news on both
"I think it is the least we expected in terms of soft tissue problems
Both are in the hamstring and both are reacting really well to treatment.
"It is difficult to tell how long it is going to take for them to get back, but I think both have got a chance to be involved at the weekend or maybe in the League Cup (when Everton face Reading away on Tuesday).
"I wouldn't rule any of the two out for the next game."
Full-back Bryan Oviedo is expected to be ready to make his return from a knee injury in the Reading fixture, while it remains to be seen exactly when Darron Gibson's first-team comeback arrives.
The midfielder featured for the Under-21s on Monday as he stepped up his recovery from a foot problem, and Martinez said of Gibson: "Medically, he's fully fit and ready to rejoin the group, it's just a case of getting him that match fitness."
The Under-21s match, a 1-1 draw with Sunderland, saw Uruguayan forward Leandro Rodriguez score for the second successive game at that level following his move from River Plate Montevideo last month.
And asked on Thursday about the prospect of the 22-year-old featuring for the Everton first-team, Martinez said: "I've been very impressed with him and I don't expect him to be too far away from being in contention."
Source : PA
Source: PA