The likes of Joleon Lescott, Micah Richards, Jack Rodwell and Edin Dzeko have all been linked with loan or permanent moves in the mid-season transfer window.
Pellegrini insists all remain important members of his squad and he has no intention of letting any move out.
Striker Dzeko, who has struggled for game time due to the form of Sergio Aguero and Alvaro Negredo, was suggested as a potential Arsenal target in reports recently.
Asked specifically about the Bosnian, Pellegrini said: "I am not thinking about that. There are a lot of rumours that are not true.
"The squad we have had from the beginning is the squad we need so it would be very strange that one player can go out in January."
Centre-back Lescott is now in the final year of his contract while fellow defender Richards has put off signing a new deal as he bids to secure a regular first-team place.
Midfielder Jack Rodwell has struggled to make an impression at the Etihad Stadium due to a succession of injuries since his move from Everton last year.
Speculation has increased around City English players as there is a perceived threat to their prospects of playing at next summer's World Cup if they are not first-team regulars.
But when asked if any of them might move, Pellegrini said: "No, they will remain here in the squad.
"Lescott has been playing the last games, Micah Richards has had injuries half of the season but he played against Plzen in the Champions League and he played against Sunderland.
"Of the last four games he has played two, so the English players, Spanish players, Argentinian players are all part of our squad and we need all of them.
"Rodwell also has been injured, maybe three or two and a half months of the season."