West Ham head to Eastlands on Sunday knowing the writing is on the wall for their future in the top flight.
The Hammers are bottom of the league and have lost their last four matches.
City are fourth, four points clear of Tottenham. They maintained their push for a Champions League spot with a 1-0 win over Blackburn on Monday.
It was also their 15th clean sheet, the equal best in the division, with Manchester United and Chelsea. City have also conceded only 30 goals, just three more than Chelsea.
Spurs are at Chelsea on Saturday and Arsenal face leaders Manchester United on Sunday.
If all three games go to form, City would be seven points clear of Tottenham with four games to play and just two points behind the Gunners with a game in hand.
West Ham, meanwhile, are looking worryingly at relegation to the Championship following six seasons in the Premier League.
When the Hammers were last relegated, in 2003, they won three and drew one of their last four games but still went down.
They amassed 42 points that season but still could not avoid the drop. They have won just 13 of their 32 points away from Upton Park.
Manager Avram Grant cannot use Wayne Bridge at City as the defender is on loan from Eastlands and is ineligible.
Mark Noble, who damaged a stomach muscle in the 3-0 defeat at Chelsea, is out for three weeks while Scott Parker is also a likely absentee, meaning West Ham will be short of midfielders.
West Ham are hoping Matthew Upson recovers from the chest infection that ruled him out of the loss at Stamford Bridge.
Even owner David Sullivan fears the worst.
After City, West Ham face relegation rivals Blackburn and Wigan before finishing at home to Sunderland, who should have little riding on the game.
Sullivan added: “We still have at least a 25-30 per cent chance of staying up so all is not yet lost.”
City manager Roberto Mancini will have one eye on the FA Cup final at Wembley against Stoke City in two weeks.
Carlos Tevez is still receiving treatment for a hamstring injury and he has been given an ultimatum that he must return against Tottenham on May 10 if he is to be considered for the final.
One player keen to add to his match-winning performance against Blackburn will be striker Edin Dzeko.
The Bosnian will be keen to start against the Hammers and impress Mancini with the FA Cup showdown in mind.
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