The England international was left out of the lineup that secured a 2-0 victory over Newcastle United in the Capital One Cup at St James' Park last night.
There have been suggestions that Hart should be dropped from this weekend's Premier League fixture against Norwich City due to a number of blunders over the past few weeks.
Costel Pantilimon, who took the number one role in yesterday's cup tie, is being considered by Pellegrini to start at the Etihad Stadium on Saturday.
"I think that we will talk tomorrow [about team selection]," the Daily Star quotes Pellegrini as saying. "One goalkeeper can play but the other will have our full support. We will think about it."
City are currently seventh in the league table after nine games.