The Dublin Bay South TD also said he would not rule himself out and that he is “interested” in being the next leader of the party.
Speaking on This Week on RTÉ Radio One, he was asked does he think Mr Martin would lead the party into the next election if the Government was to last full term until 2025.
“If [this Government] goes full term, we’re talking about 2025. Obviously, I’m conscious that Micheál Martin doesn’t want to say anything that can undermine his current position and I don’t want to contribute to that.
“But I would have thought that it’s unlikely that in 2025 Micheál Martin would be leading Fianna Fáil into an election, that’s just my own view,” he said.
Mr O’Callaghan said he is not “going to rule myself out” and that it would be a “great privilege” to lead the party.
“I was asked before whether or not I was interested in being the next leader of Fianna Fáil - I am, I said that, I’m not going to rule myself out, that would be a great privilege, I believe that’s an honour and a privilege that virtually every member of the Fianna Fáil parliamentary party shares with me.
“I’m not going to do anything just for the sake of trying to undermine the leader or trying to give an impression to the media that I believe there is something going on when I don’t believe there is,” he said.
He was speaking after TD Barry Cowen sent a letter to members of the parliamentary party yesterday urging for a post-mortem not just on the by election but last year’s general election is
Mr O’Callaghan said that Deputy Cowen seeking an in-person meeting of the PP is “so important and so useful”.
“We need to engage with the issues and try to figure out why it is we’re not resonating with the Irish public, who share our values,” he said.
“We need to look at much more fundamental questions.”
Meanwhile, Minister for Education Norma Foley said on RTÉ's The Week in Politics that there is no widespread support in the party for a heave against the Taoiseach.
When asked if 10 TDs would be willing to sign a motion of no confidence in Mr Martin, she said: “No, not at all.”
“There’s a responsibility on all of us, including the grassroots, to get down to the job of work that needs to be done in terms of the party,” she said.
Minister Foley said that Mr Martin can “absolutely” lead the party into the next election.