According to the BBC, Hart, 26, has missed the last five City games after being dropped but is set to play against Viktoria Plzen in the Champions League on Wednesday.
Pellegrini said that there is a lot of news about six or seven goalkeepers that they want to buy it is not true.
He added that there is no chance that Joe Hart could go out of the squad in January.
Hart lost his first-team place after a mistake against Chelsea led to Fernando Torres scoring a winner as City were beaten 2-1 at Stamford Bridge on 27 October, the report said.
He played for England in their 1-0 defeat by Germany in an international friendly on 19 November but has seen his club spot taken by Romanian Costel Pantilimon, the report added.