DUP party officers are expected to meet as early as Saturday to agree a timetable for choosing a new party leader.
Jeffrey Donaldson is widely regarded as the most likely to succeed Edwin Poots, who announced on Thursday night he was standing down less than five weeks after his election.
A senior DUP source told The Irish Times nominations were expected to open on Monday and Mr Donaldson could be appointed by Friday.
The source said there was no appetite within the party for another potentially damaging leadership election, and with Mr Donaldson expected to be the only candidate, it would be a “coronation” rather than a contest.
It is understood the party wants to move quickly to appoint a new leader in order to try and heal the divisions within the DUP.
“We want to regain the confidence of the electorate out there and restore our position,” the source said. “It’s about uniting the party and moving forward as Team DUP.”
On Friday night there had been no official confirmation from the DUP of the timetable for the election of a new leader.
In his resignation statement on Thursday, Mr Poots said he had asked the party chairman to "commence an electoral process within the party to allow for a new leader of the Democratic Unionist Party to be elected."
He said he would remain in the post until his successor was chosen.
His close ally Paul Givan remains in the post of Northern Ireland First Minister.
Mr Poots’s position as DUP leader became untenable after he defied a substantial majority of his party’s MPs and Assembly members and pushed ahead with the nomination of Mr Givan as First Minister on Thursday.
It followed a heated meeting in which MLAs, who were joined by three MPs, made clear he did not have their backing following a compromise deal on the introduction of Irish language and other cultural legislation brokered by the Northern secretary, which averted the potential collapse of the Assembly.
Sinn Féin agreed to make a nomination to the post of deputy first minister on the basis of the deal, which was opposed by many DUP representatives, who felt it was a capitulation to Sinn Féin.
On Friday night, the Loyalist Communities Council, which represents loyalist paramilitary organisations the Ulster Defence Association (UDA), Ulster Volunteer Force (UVF) and the Red Hand Commando, called on the new DUP leader to collapse the Assembly if necessary to "stop the constant flow of concessions to Sinn Féin".
Citing what it described as “recent instances of capitulation to Sinn Féin blackmail” and the continued lack of progress in removing the Northern Ireland protocol, the council called for a “united unionist response to vigorously resist these attacks on unionism.”
At a crossroads
Speaking to reporters on Friday, the North’s Deputy First Minister, Michelle O’Neill, said the DUP was a “crossroads” and had a choice to make over the party’s commitment to powersharing.
“I think the issues for the DUP are for the DUP, but where I’m concerned is where it impacts on the day-to-day governance,” Ms O’Neill said.
“That’s where I would have concerns. So I hope that they get to the point where they’re able to resolve their internal issues, and we get back to basics and dealing with good powersharing and delivering public services.”
She did not rule out an early election, saying that it was “hard to say what’s going to happen next within the DUP. I hope that we are able to continue to share power.”
“If we run to the end of the mandate, well and good. If there has to be an election before that, then we will fight that election.”
The Alliance, the SDLP and the UUP also called for the DUP to commit to powersharing and to work with the other parties for the benefit of people in Northern Ireland.
UK prime minister Boris Johnson told the BBC it was "very important that the Northern Ireland government should be stable, it should enjoy support from across parties, which it does and that's good. It's back up and running."