Jagielka has not played since late February because of a hamstring problem, while fellow defender Distin missed Saturday's 2-0 loss at Southampton due to a similar complaint.
And Martinez told evertontv on Tuesday: "Phil has done really well in his programme and has developed strength in his muscles.
"He looks completely regenerated and is desperate to be available.
"It will be a late call whether he is available or not but I would be surprised if he doesn't make the squad for Saturday.
"Sylvain Distin again is pushing himself to be available.
"We need to carry on with the programme that he has and make sure that the treatment is bringing a good effect.
"I would say he is 50-50 for the weekend but now we have hope that we will see Sylvain before the season ends, which is a fantastic bonus."
Everton announced on Monday that full-back Leighton Baines - another England international, like Jagielka - is set to be fit for the City contest despite picking up knocks to his knee and calf during the Southampton game.
Martinez added: "Leighton did incredibly well on Saturday to be on the pitch after having a knock because he had some discomfort in his knee.
"We had the tests and the scans, and everything is very positive.
"He's going to be treated over the next few days to see how he responds but we don't expect any major problem, so hopefully he can be involved in Saturday's game."
Source : PA
Source: PA