A run of just one win since Boxing Day means City go into the weekend with just four points' breathing space on the bottom three.
Victory for Villa would take them to within a point of their hosts with just six games left of the season, but Jerome has called for calm ahead of the weekend.
He said: "Villa are right in the relegation mix.
"Whilst we know we aren't clear of that threat either just yet, it is a game Villa know they really have to win.
"There are seven games to go and a lot of points to be played for, so obviously we want to pick up as many points as possible during that time.
"It's not do or die for us though, not at all, but we do understand the need of getting a win under our belts to give us a bit more breathing space, and in many ways take some of the pressure off."