Sinn Fein President Gerry Adams is expected to nominate Ian Paisley as Northern Ireland's first minister amid efforts to restore devolution.
The 108 assembly members met on 15 May
Mr Paisley was entitled to the post of First Minister under the terms of the Good Friday Agreement, said Mr Adams.
But the DUP leader has already made it clear that he will refuse to accept Mr Adams's nomination.
Monday's vote will follow an address to Stormont assembly members by Scottish First Minister Jack McConnell.
Northern Ireland Secretary Peter Hain invited Mr McConnell to Belfast to "highlight the benefits of devolution".
Mr McConnell said on Monday that he was not in Northern Ireland to lecture assembly members, but to offer evidence on the advantages of devolution.
"I believe that by working together we can learn from each other," he said.
"We have made great progress under devolution in Scotland. Scotland is a far better country today than it was seven years ago."
Speaking ahead of Monday's assembly session, Mr Adams said he would nominate the DUP leader and Martin McGuinness to the positions of first and deputy first ministers respectively.
"Ian Paisley has the right to the post of First Minister under the terms of the Good Friday Agreement," he said.
NI Secretary Peter Hain gave deadline of 24 November
"It may be that Ian Paisley will refuse to accept a nomination at this time. That is his choice.
"But as Sinn Fein has said numerous times the only reason we are participating in the 'Peter Hain Assembly' is to get the power sharing executive re-established."
UUP leader Sir Reg Empey said that if the election for the first and deputy first minister posts did not take place, he hoped the assembly would be able to debate a motion on Tuesday calling for the establishment of a committee for the restoration of devolution.
"Tuesday represents a crucial day. The assembly could establish a mechanism that will allow us to concentrate on the main business which is to establish whether it is possible to get devolution or not," he said.
"We understand that there are many social and economic matters that we wish to debate, however none of that can replace the fundamental duty on the assembly to focus on the obstacles on the restoration of devolution."
No-one expects the vote on forming a power-sharing government to go through, but under the new temporary rules of this assembly, it will still be possible for the politicians to debate other matters.
On 15 May, Northern Ireland's politicians took their seats in the Stormont assembly for the first time since October 2002.
While there is no immediate prospect of a power-sharing executive being formed, the government hopes recalling the politicians will help to pave the way towards a deal in the autumn, by its deadline of 24 November.
Devolved government was suspended over allegations of a republican spy ring. The court case that followed collapsed.
Direct rule from London was restored in October 2002 and has been in place since.
Under the temporary rules, policy matters can be debated, but laws cannot be made.