Taoiseach Enda Kenny must fill two Irish vacancies in eminent European bodies before the summer. In question now is whether any Cabinet change is in prospect as a result.

The first vacancy is for Ireland's seat on the board of the European Bank for Reconstruction and Development (EBRD), a non-EU institution based in London which supports private lending in the former Soviet bloc. This has been occupied since 2010 by former Fianna Fáil MEP Eoin Ryan. His term expires in June.

The second is for Ireland's seat on the bench of the European General Court, a division of the European Court of Justice in Luxembourg and formerly known as the European Court of First Instance. The current Irish member is Mr Justice Kevin O'Higgins. His term expires in August.

Although appointments to the court are renewable, the judge was told last month the Government would not renominate him. In parts of the Coalition, this decision was interpreted as part of a sequencing manoeuvre to ensure an easy division of spoils between Fine Gael and Labour when the EBRD appointment is made.

These vacancies loomed even before Labour's dismal showing in the Meath East byelection prompted talk of Tánaiste Eamon Gilmore leaving Foreign Affairs to take an economic portfolio.

Both a rejig within the Labour flank of the Cabinet and an exchange with Minister for Enterprise Richard Bruton have been mooted. Bruton would not like that, and his proximity to IDA Ireland job announcements is as precious to Fine Gael as it would be to Labour.

Whispers of a change for Gilmore – which found their way into news copy – reflect profound unease within Labour at its waning public support. Yet there is little sympathy in Fine Gael for Labour hand-wringing, the argument being that the junior partner should just get on with what is an exceedingly difficult job.

The Taoiseach’s preference, it is said, is to wait until after the local and EU elections next year to recast the administration by way of a reshuffle. To maintain his authority, this is a tool he can deploy only once. Given the Government’s lack of popularity, it is one he would much rather keep in reserve until after the elections.

Yet while the situation within Fine Gael appears stable, Labour is still prone to shock. It remains to be seen whether the combination of the Croke Park II process, the property tax and the water tax stoke further jitters among its TDs. These are questions, after all, that tend to hurt its core support the most. For the moment, talk of early moves around the Cabinet table is routinely dismissed. What cannot be rubbished so easily is the fact that two plum jobs, in London and Luxembourg, must be filled within a matter of months.

So where is the betting? The sense around Leinster House is that the court position may go to a member of Labour’s legal fraternity. This is grounded in the fact that Judge O’Higgins comes from a family with impeccable Fine Gael credentials. He is in his fifth year in Luxembourg and is said to have been keen for a second term. It was not to be, fuelling anticipation that the job will go to a legal figure associated with the smaller party.

Even greater intrigue surrounds the EBRD position, which commands a salary of some £140,000 (€164,300) and attractive tax provisions. Some politicians believe Minister for the Environment Phil Hogan may be a contender, the thinking being that his portfolio is proving to be quite a challenge and consistently so.

There was, for example, the appearance of a misstep on water tax with his indication that the charge will be levied from the start of 2014. Gilmore dismissed that within days. Minister for Finance Michael Noonan weighed in behind Gilmore, although Noonan did make the important point that money not collected would have to be found elsewhere.

Part of the reason for the speculation around Hogan is that he is said to have designs on Ireland's seat in the European Commission, which comes up next year. If a move into the international arena is of interest to him, would he go to London instead of Brussels? Hogan is a political heavyweight and ably deployed his muscle in Kenny's defence of his Fine Gael leadership against the Bruton heave. Kenny's sense of loyalty is well established but whether the Taoiseach would grant him the commission seat is another matter.

Given the trauma of the bailout, Ireland’s central interest lies in securing a senior post in the EU executive next time round. Some in Government circles believe Hogan, who does not demonstrate any great interest in European affairs, is not the man for that. But a further consideration is that the exit of any elected Government figure to the EBRD would necessitate another byelection. The Meath East mauling suggests Labour would rather run a mile from another opportunity for the public to demonstrate its lack of affection – and Fine Gael might not be that far behind either.

The concern centres more on the destablising impact of an electoral black eye than on the probable loss of a Government seat per se . Some well-placed figures say this is the prime question right now.

Another potential name is Gay Mitchell, outgoing Fine Gael MEP for Dublin. This avoids any problem with byelections but his feeble showing in the presidential election raises questions.

The likelihood is that Kenny will not rush these nominations. The failure to nominate a successor to the late Shane McEntee as minister of state for agriculture is instructive. That appointment, said for many weeks to be imminent, remains imminent.