The Toffees could aid rival Liverpool's bid for the Premier League title by maintaining their impressive record against Manuel Pellegrini's men but their form has faltered of late.
Manuel Pellegrini's side took over as the favorite to be crowned champion when it won 2-0 at Crystal Palace after Liverpool was beaten by Chelsea on Sunday. Although City is third in the table, it is just three points behind Brendan Rodgers' league leader and one adrift of the Blues with a game in hand on the top two.
City also boasts a superior goal difference to their rivals, a factor that could yet prove crucial as it did in the team's title triumph two seasons ago.
Pellegrini's men will fancy their chances of winning their final two matches at home to Aston Villa and West Ham but can expect a stern test at Goodison Park.
Roberto Martinez's side appears to have blown its chances of securing a Champions League spot, having fallen four points behind fourth-placed Arsenal following recent defeats to Crystal Palace and Southampton.
However, is could all but seal fifth spot - and a place in the Europa League - by doing neighbor Liverpool a favor and inflicting a damaging defeat on City.
City's title hopes were dealt a major blow when they were beaten 3-2 at Anfield in April but the Blues return to Merseyside three weeks on with their destiny in their own hands and midfielder Fernandinho believes that the momentum is with Pellegrini's side following the last round of results.
"[The title race] changed a lot," the Brazil international told City's official website. "We are back with a big chance of being champions again.
"We are not depending on other teams - it only depends on us, and that has changed a lot.
"It gives you energy as mentality is 70 percent of your body, and a result like that changes everything – your mind, your motivation, everything.
"We have waited a long time for this moment and the positivity of the whole group is now very high. I think we will get better and better until the last game, and then we must see what happens at the end of the season."
City could be boosted by the return of playmaker David Silva (ankle) but it is unclear whether or not Jesus Navas (ankle) and Matija Nastasic (knee) will play any part.
Everton captain Phil Jagielka is poised to make his long-awaited return from a hamstring injury and fellow center back Sylvain Distin could also feature after missing their defeat at Southampton due to a hamstring problem of his own. Gareth Barry will play no part, though, as the on-loan midfielder is ineligible to face his parent club.