Pellegrini's men twice gave back leads established by Sergio Aguero and Kevin De Bruyne to be held to a 2-2 draw by Arsenal at the Etihad Stadium last time out, meaning victory for United in east London would have lifted Louis van Gaal's side into the top four before their home match with AFC Bournemouth.
Instead the impetus lies with City, whose vastly superior goal difference effectively means they need only avoid defeat to retain their top-four place.
And ahead of Sunday's crunch match, Pellegrini has urged his side to maintain their focus against opponents who have impressed with convincing victories over Liverpool and West Ham United.
Aguero and Ranieri win Barclays awards for April >>
"It's always a difficult game when you play away," Pellegrini told his final pre-match news conference before he makes way for Pep Guardiola.
"Swansea has done very well in the last two games. We had an atmosphere when everybody thought we were eliminated from the first four positions.
"I am sure in the future this club will continue growing."
Sunday's match comes days after Swansea City announced they would retain Francesco Guidolin on an extended two-year contract.
The Swans head coach said: "It is not easy to keep going up in football. It is important to have a season that is complicated to understand and learn new things."
City remain without captain Vincent Kompany (thigh), fellow defender Pablo Zabaleta (calf) and playmaker David Silva (hamstring), while Aleksandar Kolarov (muscular) and Samir Nasri (illness) will be assessed.
Swansea goalkeeper Lukasz Fabianski will join team-mates Ashley Williams, Neil Taylor and Gylfi Sigurdsson in resting up ahead of Euro 2016 commitments, meaning a likely Barclays Premier League debut for Kristoffer Nordfeldt.
Swansea City (from): Nordfeldt, Vickers, Zabret, Amat, Bartley, Fernandez, Naughton, Rangel, Ayew, Britton, Cork, Fer, Fulton, Grimes, Ki, Lucas, Montero, Routledge, Barrow, Emnes, Gomis, Paloschi.
Manchester City (from): Caballero, Hart, Wright, Clichy, Demichelis, Kolarov, Mangala, Otamendi, Sagna, De Bruyne, Delph, Fernandinho, Fernando, Nasri, Navas, Toure, A Garcia, M Garcia, Aguero, Bony, Iheanacho, Sterling, Celina.
Match Appointments
Referee: Mike Dean Assistants: J Collin, S Long Fourth Official: A Marriner
Match Facts
- Wilfried Bony has scored in both of his Barclays Premier League matches against former club Swansea City, and netted three goals in his last two appearances for the Swans against Man City before that.
- Manchester City have won six and lost none of the last seven BPL meetings with Swansea.
- Yaya Toure has scored four goals in his last four league appearances against Swansea.
- The Swans have won their last four BPL home matches, their best run of home results in the history of the competition.
Instead the impetus lies with City, whose vastly superior goal difference effectively means they need only avoid defeat to retain their top-four place.
And ahead of Sunday's crunch match, Pellegrini has urged his side to maintain their focus against opponents who have impressed with convincing victories over Liverpool and West Ham United.
Aguero and Ranieri win Barclays awards for April >>
"It's always a difficult game when you play away," Pellegrini told his final pre-match news conference before he makes way for Pep Guardiola.
"Swansea has done very well in the last two games. We had an atmosphere when everybody thought we were eliminated from the first four positions.
"I am sure in the future this club will continue growing."
Sunday's match comes days after Swansea City announced they would retain Francesco Guidolin on an extended two-year contract.
The Swans head coach said: "It is not easy to keep going up in football. It is important to have a season that is complicated to understand and learn new things."
City remain without captain Vincent Kompany (thigh), fellow defender Pablo Zabaleta (calf) and playmaker David Silva (hamstring), while Aleksandar Kolarov (muscular) and Samir Nasri (illness) will be assessed.
Swansea goalkeeper Lukasz Fabianski will join team-mates Ashley Williams, Neil Taylor and Gylfi Sigurdsson in resting up ahead of Euro 2016 commitments, meaning a likely Barclays Premier League debut for Kristoffer Nordfeldt.
Swansea City (from): Nordfeldt, Vickers, Zabret, Amat, Bartley, Fernandez, Naughton, Rangel, Ayew, Britton, Cork, Fer, Fulton, Grimes, Ki, Lucas, Montero, Routledge, Barrow, Emnes, Gomis, Paloschi.
Manchester City (from): Caballero, Hart, Wright, Clichy, Demichelis, Kolarov, Mangala, Otamendi, Sagna, De Bruyne, Delph, Fernandinho, Fernando, Nasri, Navas, Toure, A Garcia, M Garcia, Aguero, Bony, Iheanacho, Sterling, Celina.
Match Appointments
Referee: Mike Dean Assistants: J Collin, S Long Fourth Official: A Marriner
Match Facts
- Wilfried Bony has scored in both of his Barclays Premier League matches against former club Swansea City, and netted three goals in his last two appearances for the Swans against Man City before that.
- Manchester City have won six and lost none of the last seven BPL meetings with Swansea.
- Yaya Toure has scored four goals in his last four league appearances against Swansea.
- The Swans have won their last four BPL home matches, their best run of home results in the history of the competition.
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