He would be Japan's oldest prime minister on entering office since 1991. Abe, who at 53 was Japan's youngest leader in recent times, was criticised for being too inexperienced.
While campaigning in the north of the country, Fukuda said: "I want to get people to think that the LDP and politics as a whole are truly getting better by resolving problems one by one."
Japan's next leader will face a divided parliament, with combative opposition parties controlling the upper house, and conflicting pressures to spend more to woo disaffected voters.
He must also try to rein in his country's huge public debt.
The situation has raised fears of a policy deadlock at a time when Japan needs action on pensions, taxation and other issues.Economic reforms
A survey by Kyodo news agency published late on Saturday showed Fukuda well ahead of Taro Aso, the conservative ex-foreign minister, in the party poll. Other surveys have shown similar results.
The winner will be chosen as prime minister on Tuesday by virtue of the ruling camp's majority in parliament's lower house.
Critics of Fukuda, the chief cabinet secretary under Abe's popular predecessor Junichiro Koizumi, say he will be beholden to the LDP's old guard and will backpedal on economic reforms.
Fans say his milder style will be welcome after Koizumi's five years of combative reforms and 12 months of scandals under Abe.Rural focus
Both Fukuda and Aso have pledged to pay more heed to rural regions and other sectors hurt by policies begun under Koizumi.
One of the new prime minister's priorities will be to avoid the pitfalls that could result in a snap election for the lower house, which the ruling camp could well lose.
No general election need be held until 2009. But a deadlock in parliament could prompt one and many are eyeing next spring, after passage of the budget for the fiscal year starting next April, as a likely time.
The winning candidate in the LDP poll needs a majority, or 265, of 528 votes comprised of 387 parliamentarians and three representatives from each of the party's 47 prefectural chapters.