* Kenny has said he will not lead Fine Gael in next election
* Calls for prompt handover grow as party's support slumps
* Contender wants that to happen after March 17 U.S. visit (Adds fin min comments)
By Padraic Halpin
DUBLIN, Feb 20 (Reuters) - Ireland's finance minister said on Monday he expects Prime Minister Enda Kenny - who has already said he will not lead his party into an election due next year - to say on Wednesday when he will step down.
With calls increasing for Kenny to spell out his plans, his spokesman said he would not comment until a meeting of his Fine Gael party on Wednesday.
Finance Minister Michael Noonan said he assumed Kenny would provide a timetable at the meeting.
Kenny, prime minister since 2011, leads a minority government that has become increasingly unstable and only narrowly survived a vote of no-confidence last week over its handling of a policing scandal.
One of the two top contenders to take over the centre-right party said on Sunday that a new leader should be chosen after Kenny's trip to Washington for the annual meeting with the U.S. president to mark St. Patrick's Day on March 17.
"I think after that visit you will see, I hope, an orderly and quite a quick transition to new leadership within Fine Gael," Housing Minister Simon Coveney told national broadcaster RTE.
Calls for such a transition that would head off a possible vote of no confidence in Kenny's leadership have gathered pace since support for the party slumped. Fine Gael fell to second place in an opinion poll on Sunday, eight points behind its main rival Fianna Fail.
Kenny's government, which includes a number of independent lawmakers, relies on Fianna Fail to abstain in key votes to govern.
Fianna Fail's leader warned last week that the arrangement was under serious strain and a frontbench spokesman on Monday called on Fine Gael to deal quickly with the leadership issue.
Kenny, who has led his party since 2002, is expected to hand over to a much younger leader. The main contender other than 44-year old Coveney is 38-year-old Social Protection Minster Leo Varadkar.
Once endorsed by parliament, Kenny's successor would also lead Ireland's negotiations within the European Union over Britain's departure from the European Union, a two-year process due to begin at the end of next month.
Ireland is considered the EU economy most at risk from its key trading partner and near neighbour's decision to quit the bloc. (Editing by Robin Pomeroy)