Peter Robinson has warned his former colleagues not to expect all their demands around post-Brexit trade arrangements to be met by the British government.
In an intervention widely regarded as signalling the need for the DUP to strike a compromise, the former first minister suggested the assembly was the most effective forum for negotiating changes to the Northern Ireland Protocol.
His remarks have heightened expectations that the DUP's 21-month boycott of the institutions is nearing its end.
Mr Robinson said he believed a "gap" still exists between the DUP and the UK government but that he hoped differences could be resolved soon.
His remarks came a matter of days after Taoiseach Leo Varadkar voiced optimism about the potential return of the Stormont institutions before Christmas or early in the new year.
The DUP collapsed devolution in February last year in protest at the Northern Ireland Protocol. February's Windsor Framework deal between the UK and EU was designed to assuage unionist concerns, however, the party is seeking further assurances around Northern Ireland's place in the UK single market.
Secretary of State Chris Heaton-Harris has said talks which the DUP hopes will result in Westminster legislation are in their final phase.
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In an interview with the BBC, Mr Robinson said he hoped a deal could be agreed "within the next number of weeks".
"There's a stage where unionists have to recognise that we really have pushed this one, we have got a good deal - not everything that we wanted but the rest that we do want I think we're in position to argue for it and to achieve it using the assembly as our base for doing it," he said.
The former first minister was critical of unionism's strategic approach.
"Nationalists and republicans look at what their objective is, each step they take they look to see - does that take us closer to our objective," he said.
"Unionists and loyalists think they should clear the table in one visit, to use a snooker analogy, but that's not always possible – what you want to do is make sure you have a sufficient score to enable you to clear the table when next you go to it."
But DUP MP Sammy Wilson, widely regarded as being among a number of party hardliners, said the objectives sought in the negotiations had yet to be met.
"You have to see the nature of the deal to decide whether it is a good deal or not," he said.
Sinn Féin MLA Conor Murphy said people had been left to suffer due to "dysfunctionality" within the DUP.
He said Mr Robinson's comments indicated "a degree of choreography going on".
"While the rest of us wait, programmes suffer and public services suffer, people have an uncertain economic future and the cost-of-living crisis is continuing to bite families and workers, the DUP continue to play this out," Mr Murphy said.
A DUP statement said: "Peter Robinson is giving a series of interviews promoting his new book and his own views and analysis are shared by him on the basis of years of experience. He has not claimed to be speaking on behalf of anyone other than himself.
"The party's position is a matter of record.
"Our discussions with the government continue and agreement has not yet been reached. This is a time for cool heads.
"We will judge any outcome against our clearly declared objectives of restoring our place in the union and our ability to trade within the UK and its internal market."
