City lie third in the Premier League, three points behind leaders Chelsea with a game in hand, and have a League Cup final against Sunderland and an FA Cup quarter-final with Wigan Athletic to come in the next two weeks.
However, Manuel Pellegrini's men face a huge task to progress further in the Champions League, having lost the first leg of their last 16 tie with Barca 2-0 at the Etihad Stadium.
But Navas, who City felt was fouled in the build up to the Catalans' first goal last Tuesday, remains optimistic of a historic quadruple.
"We are still alive in everything," the Spain international told the Manchester Evening News.
"I think we have a good enough team to have a chance in all four. We will fight to the end.
"There are a lot of games. But the reason is because we are battling on every front. It's not a complaint.
"I think we can go there (Barcelona) and make a statement.
"We can go and do something very important. It's possible.
"I think we can go and give a good account of ourselves. We will fight to the end."
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