Health Secretary Vaughan Gething has told BBC Wales he is "optimistic" he can be a candidate to be the next first minister and leader of Welsh Labour.
It follows four Labour AMs saying they will back him - he needs five nominations to stand. Currently only Mark Drakeford has enough support.
Mr Gething called for "renewal", saying Labour would not win a majority in 2021 by offering "more of the same".
Carwyn Jones is stepping down after nine years in charge later this year.
Finance Secretary Mark Drakeford has already announced he will stand and with eight names behind him has the necessary support to enter the contest.
Mr Gething told BBC Wales he was "delighted" to have his colleagues' support.
"I'm obviously considering and I would like to be in the race to be leader of our party and our country," he said.
"I can't take anything for granted. It doesn't mean I will be a guaranteed part of the contest."
"We're in the fortunate yet challenging position of having had Welsh Labour leadership for nearly 20 years," the Cardiff South and Penarth AM added.
"That's a remarkable achievement. But it brings its own challenges as well about how we renew in government," he said.
"If we want to win a historic first time ever majority we have to recognise we can't simply say you've had 20 years of us, expect a lot more of the same.
"I don't think that's an attractive message."
He denied that the comments were "setting out a stall to negatively go after other people".
Mr Drakeford, who declared his candidacy shortly after Mr Jones announced in April that he was stepping down, has indicated he would not want to change the direction of the party in a significant way.
He told BBC Wales in April that Welsh Labour "would not change course radically because it has a new first minister because we made a series of promises".
He said he would bring a "series of new emphases to the job".
Mr Gething's confirmation that he hoped to be a contender came after he was publicly backed by Hefin David, Lynne Neagle, Joyce Watson and Vikki Howells.
In an open letter, they said there should be a candidate who understands the "unique Welsh Labour history" and is ready to renew the party while in power.
"Welsh Labour will only succeed if it reflects the wonderfully diverse Wales of today," it reads.
"Our next leader must embody the optimism that we need for the future.
"They must be ready to represent all our communities, recognising that a changing Wales is an opportunity, not a threat."
The four AMs believe Mr Gething is best placed to "galvanise our movement" and guard against the "growing possibility" of a Tory-Plaid pact in the assembly.
Mr David told BBC Radio Wales he was "reasonably confident" Mr Gething would get the nominations he needed to get on the ballot paper - and denied that the letter made the health secretary look weak.
Speaking on Good Morning Wales, the Caerphilly AM added: "He is very good at harnessing ideas from a range of different sources - from AMs, party members and people outside the Labour party."
Analysis by Arwyn Jones, BBC Wales political correspondent
Unless Vaughan Gething has massively overestimated the non-public promises of support he's had from fellow Labour AMs, we will have a race to succeed Carwyn Jones, not a coronation.
It is easy to characterise this as a competition between a Corbynist candidate - Mark Drakeford - on one hand and the more centrist - if still left-wing - Vaughan Gething on the other.
The truth is that we just don't know the policies of the two men yet.
It seems to me that Mr Gething wants to portray himself as a clean break from the past, as opposed to the "continuity candidate" of Mr Drakeford.
They also differ on how the next leader should be elected; Mark Drakeford has been in favour of moving to "one-member-one-vote" while Vaughan Gething insists nothing should dilute the historic role of the trades union within the Labour Party.