Leaders of the four right-wing parties hoping to form a new Dutch government are to spend two days holding talks behind closed doors to try to decide what form the cabinet should take.

The four leaders – Geert Wilders of the PVV, Dilan Yesilgöz of the VVD, Pieter Omtzigt of NSC and Caroline van der Plas of the BBB – will meet at the Zwaluwenberg, a country estate on the edge of Hilversum, without their deputies.

The talks will be overseen by Kim Putters, chair of the social-economic council, whose findings will be presented to parliament and debated later this week.

It is the first time the quartet have sat down together in four weeks, since Omtzigt withdrew from the first round of negotiations and said he would not join a coalition with the other three.

Putters had hoped to present his report to parliament at the start of this week, but last Thursday he said further discussions were needed and he was now aiming to be finished by Wednesday. “We are on our way, but there is still a lot of ground to cover,” he said.

Speculation is growing in Dutch media that the parties will form a so-called “extra-parliamentary” cabinet, which includes ministers drawn from outside the political parties.

Omtzigt has said an extra-parliamentary administration is his preferred option, because it will be less bound by party discipline, which he argues will give MPs more scope to scrutinise ministerial proposals.

Yesilgöz has also expressed support for the extra-parliamentary option and says she is “hopeful” that a new government can be in place by the summer.

However, Wilders and Van der Plas still favour a conventional coalition of the four parties, which would have a majority in both houses of parliament.

An alternative coalition headed by the left-wing alliance GroenLinks-PvdA, led by former European commissioner Frans Timmermans, is not being seriously considered at this stage.

Both the VVD and NSC said after the election that they would prefer to support a minority government through a confidence and supply deal, rather than provide ministers as members of a coalition. The VVD is the only one of the four parties with a pool of experienced ministers to call on.