There is an opinion within the party that there is no need for two finance departments, and a return to a united Department of Finance is “being actively considered”.
Finance Minister Michael Noonan is expected to leave office alongside Mr Kenny, and Minister Public Expenditure and Reform Paschal Donohoe is being tipped to succeed him.
Ahead of the general election last year, the Fine Gael manifesto suggested the possibility of Public Expenditure and Reform (PER) being merged back into Finance.
However, the dismal election result for the party — it lost 26 seats — put that on hold. However, now a reshuffle is pending, it is being considered again, as some sources feel that the Department of Public Expenditure and Reform has become too powerful in relation to other departments.
“It probably made sense to have two finance departments during the crash, when the banks needed far more attention than they do now,” said one senior party figure. “But there is a feeling that it is hard to justify the existence of both.”
The desire to at least consider the scrapping of Mr Donohoe’s department is shared by both Social Protection Minister Leo Varadkar and Housing Minister Simon Coveney, the front runners in the race to succeed Mr Kenny as Fine Gael leader.
The Finance Department was split in two in 2011 by the incoming Fine Gael-Labour government, and Brendan Howlin was the first occupant of the office, alongside Mr Noonan.
This was because the late Brian Lenihan, the last Fianna Fáil finance minister, was overwhelmed by the workload during the crash between 2008 and 2011.
The department has been locked in numerous high-profile disputes since its inception, most notably with the Department of Health over the formation of budgets.
Meanwhile, the Government must cut tax or it risks losing jobs to other countries in the wake of Brexit, Mr Donohoe has warned. The minister said workers should not be forced to hand over half of their income to the State when they are earning low wages.
In a key intervention ahead of the forthcoming Fine Gael leadership contest, Mr Donohoe says the marginal tax rate needs to be lowered if Ireland is to remain an attractive destination.
The warning comes as reports suggest UK prime minister, Theresa May, could formally trigger Britain’s exit from the European Union on Tuesday.
Mr Donohoe again ruled himself out as a candidate to replace Enda Kenny when he steps down as Fine Gael leader on his return from his St Patrick’s Day State visit to the US.
However, Mr Donohoe’s comments could be perceived as a pitch to replace Mr Noonan. Mr Donohoe’s call for lower tax chimes with comments by Mr Varadkar, who said Fine Gael should reduce tax, because “people know best how to spend their own money, and deserve to be rewarded for work”.