Despite an injury-hit season restricting him to just 17 Premier League starts, Aguero has still struck 15 goals, fuelling rumours of a move to the Catalan outfit.
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"[My response] is exactly the same as what I respond to all the other links during the whole year," Pellegrini told reporters.
"You cannot talk every week about players that are coming here and the players going out. Aguero is a Manchester City player, he is very happy here and the club is very happy with him."
Pellegrini also confirmed that Aguero is set to miss the Manchester derby on March 25, stating: "At the end of next week he will start training with the rest of the squad."
Manchester City were recently knocked out of the Champions League round-of-16 by Barcelona, with Pellegrini receiving a two--game touchline suspension by Uefa for criticising referee Jonas Eriksson following his side's 2-0 first-leg defeat to Barca.
Los Blaugranas were drawn against Primera Division rivals Atletico Madrid in the quarter-finals of the Champions League on Friday morning.