Caballero could be in line to start against Liverpool in Sunday's final.
Pellegrini has selected Caballero ahead of Hart for both domestic cup competitions - like in 2014 when Costel Pantilimon was in goal for City for their triumph over Sunderland at Wembley.
As a result, Caballero is expected to start in goal against Liverpool on Sunday, and told Sky Sports: "I try to help him during the week because we are fighting during the week to play, but he has the opportunity to do it every week, and I try to be his supporter.
"Sometimes it is really difficult [being on the bench]. But even teams like Liverpool play just one goalkeeper in all competitions, so I feel blessed to be in this team.
"I feel the confidence of the boss to bring me into this game. I try to enjoy it, and try to improve every week. I have to be ready for this date, which will be fantastic for us.
"I think it will be a great final. We must be ready for everything, even for penalties. Beating Liverpool will be fantastic but it won't be easy, so we must play well, defend well and be solid."
It's a big occasion for both sides but it's definitely a big occasion for the City goalkeeper if he is given the nod ahead of Joe Hart, especially after being part of the side that was thrashed 5-1 by Chelsea in the FA Cup at the weekend, and has yet to register a clean sheet in the League Cup so far this season.
It has been a bit of a sticky phase for City in recent weeks so a win on Sunday, and some silverware to show for their efforts this season at the very least could be a confidence boost to the players to and challenge on the remaining two fronts.
Caballero has spoken of the need to be solid and that also goes for him. The last thing any goalkeeper will want to do is make a costly error in a cup final.