The likes of Joe Hart, Edin Dzeko, Joleon Lescott and Micah Richards have been linked with moves in the New Year, having struggled to hold down starting roles under the Chilean.
But Pellegrini is remaining firm, and when asked about those players being linked with moves, he said: "There are a lot of rumours that are not true.
"The squad we have from the beginning is the squad we need so it would be very strange that one player can go out in January."
Pellegrini insists that English stars James Milner and Jack Rodwell, along with Lescott and Richards, are all part of his plans.
"Lescott has been playing in the last few games and James Milner is normally playing," he told the Manchester Evening News.
"Micah Richards has had injuries for half of the season but he played against Plzen in the Champions League and he played against Sunderland.
"Of the last three games he played two so the English players, Spanish players, Argentinian players are all part of our squad and we need all of them.
"Jack Rodwell also has been injured maybe three months of the season, or two and a half months."
Again asked about his goalkeeping situation, with Hart currently playing number two to Costel Pantilimon, he added: "I think it is very important to have two good goalkeepers.
"Joe Hart continues to be the number one of England, and he is a very good goalkeeper.
"But Pantilimon has played seven games, five in the Premier League and two in Capital One, and the opponents have scored just one goal, at Sunderland, so that is also important for the team.
"They are two important goalkeepers, and I trust in both of them.
"At the moment I am playing Pantilimon but you saw the other day when Joe Hart played he did very well."