Loan signing Traore has been declared fit by the club's medical staff and it would only be lack of match fitness that would prevent him from starting at White Hart Lane.
Martinez has been pleased with the giant striker in training and will probably include him on the bench for the first time on Sunday.
The boss said:
Lacina is progressing really well, I just need to assess whether it is wise to give him playing time.
He is fully fit from a medical point of view it is just a matter of giving him the right playing time over the next two or three weeks because the last thing we want is for Lacina to push himself and get stretched trying to achieve the tempo of the Premier League.
He has been a breath of fresh air on the training pitch, he has a hungry approach to everything he does and so we are excited to see him fully fit.
Martinez also confirmed that Seamus Coleman is contention to start after recovering from a hamstring injury, the Ireland man made the bench against Aston Villa last weekend but didn't come on.
However, the injury may actually work in his favour as it allowed him to return home over the traditionally attritional Christmas period, giving himself a mental break as well as a physical one.
He [Deulofeu] looks like a fresh man but a player who has never been away from Everton and that excites me.
I see the team now, after a little bit of a dip in terms of numbers, are going to be strong as we can be in the next few weeks which is really exciting.
Seamus Coleman has come through training really well. Antolin [Alcaraz] is going to be out of the weekend but it’s nothing to be worried about, it’s just trying to get him back to full fitness and Romelu Lukaku is going to be out this weekend and probably the week after, so it’s a couple of weeks for him, I don’t expect it to be any longer.
Alcaraz and Lukaku aside it is only the long-term absentees Gibson, Kone and Oviedo that are missing, giving rise to optimism that the worst of the club's injury crisis is now over.
Phil Jagielka, Sylvain Distin, Ross Barkley and Steven Pienaar have all returned to fitness over the past fortnight and their return couldn't have come at a better time with Sunday's game at Spurs one of the most crucial of the season so far.