It comes after Enda Kenny appeared to extend the deadline for his departure by saying Brexit negotiations and talks in Northern Ireland are his key priorities.
Housing Minister Mr Coveney, who along with Leo Varadkar, is seen as a top contender to take over the leadership of the party, told the Irish Examiner that too much had been made of Mr Kenny’s remarks.
“I don’t think that anything has fundamentally changed here, except that the triggering of Article 50 has been pushed back by a few weeks. I think people in Fine Gael are happy to let Enda Kenny put a process in place. Whether it’s now or a couple of weeks’ time doesn’t make a major difference.”
However, he added that it is “very unlikely” that the leadership issue would drag on over the summer.
“I don’t think this is going to be a prolonged process that goes on for months.”
Mr Coveney said he was not surprised that Mr Kenny would cite the agreement of the EU’s Brexit negotiating stance as a priority as it had long be expected that he would attend the first European Council meeting after Article 50 is triggered.
He also highlighted the success of the Taoiseach’s US trip, during which Mr Kenny raised the issue of immigration with US President Donald Trump.
Over the weekend Mr Varadkar also said the “diplomatic success” of Mr Kenny’s trip should not be “marred by talk of the leadership contest”.