Veteran defender Sylvain Distin, who is 36 next week, is entering the final six months of his deal but is set to get a short-term renewal while midfielder Ross Barkley, who turned 20 last week, is likely to get improved terms on the four-and-a-half-year contract he signed in December 2011.
Everton hope the contractual negotiations after the festive period will also include defender Leighton Baines, who is sidelined with a broken toe but is a target for Manchester United.
With 18 months remaining on the England left-back's current deal Martinez is wary of talking too much publicly about the 29-year-old, but Press Association Sport understands talks are ongoing about his future.
But with former boss David Moyes lurking in the background the Toffees' first challenge may well be to fend off a Red Devils bid in January and then persuade Baines to commit his future to them.
The situation with Barkley and Distin is more clear-cut.
"You can imagine we are working always behind the scenes to try to reward youngsters who do well at at the club and Ross is clearly that, but there is nothing to announce," said the Spaniard.
"Even when you don't speak about issues we work really hard behind the scenes to try to make sure that the youngsters get rewarded and Ross clearly deserves that.
"Sylvain has been a terrific performer this season and we couldn't be happier with his role at the club.
"All these issues are vital for us and we are going to look after them straight after this Christmas period.
"At this moment all that matters is to get everyone focused in being ready to help the team and Sylvain clearly has been an example of doing that."
Baines could well make a return before the new year as he appears to be ahead of schedule in his rehabilitation.
Having sustained the injury in the Merseyside derby at the end of November, the worst-case scenario was a six-week absence.
Martinez thinks he could be back within 10 days to a fortnight, which could make him available for the December 22 trip to Swansea.
"It is one of those injuries which is so frustrating because Leighton is feeling great but when you start to do some work you realise you still have a period to heal the fracture and give it some more time," said the Toffees boss.
"I don't think he will be available for Saturday - although I wouldn't discount it - and it will more realistic for the next couple of weeks.
"This Saturday is a very important game at home (to Fulham) and then you go straight into four games in a 10-day period, which is demanding, and then we are going to be strong in the FA Cup.
"We need as many players as we can. We have lost Darron Gibson and Arouna Kone and hope we can have everyone else and it will be vital to have Leighton fully fit."