Sir Jeffrey Donaldson said that it was a case of "the sooner, the better".
Theresa May is seeking the support of the DUP's 10 MPs after losing her majority in the general election.
Both sides have been talking, but have not confirmed a deal to support a Conservative minority government.
Sir Jeffrey said that the prime minister had been "moving this process forward" and was "engaged".
He added: "I'll say this about Ulster men and Ulster women, we're no pushover."
Sir Jeffrey, the MP for Lagan Valley, was speaking to BBC Radio 4's Today after sources told the BBC that the DUP is seeking £2bn in extra funding for Northern Ireland in return for supporting the Conservatives.
He described the reported figures as "wide of the mark" and "nonsense".
"We're talking about funding across a range of issues, certainly some money for health and education and some money for our infrastructure, but certainly the scale that we're talking about is nowhere near what's being speculated in the media."
He said that would "become evident" when the agreement is published.
Sir Jeffrey also rejected criticisms that the agreement would affect the British government's neutrality in Northern Ireland's peace process.
"The deal relates to how we operate in Westminster, let me be clear on this - we're not asking the government to take sides on the devolution debate in Northern Ireland.
"We're not seeking to drag the politics of Northern Ireland onto the national stage. I've read stuff about parading and other things, none of this will feature (in an agreement)."
Sir Jeffrey Donaldson has poured cold water on reports that his party was seeking an extra £2bn in health and infrastructure spending to support a minority Conservative government.
That was - according to the Lagan Valley MP - "wild speculation" and "wide of the mark".
However, the sources for those reports were reliable.
So is it possible the DUP is now seeking to manage down the expectations of its supporters?
Read more here.
His comments came after political parties in Northern Ireland raised concerns that ongoing DUP-Tory talks are undermining the negotiations on restoring devolution at Stormont.
The government has set a 29 June deadline for a Stormont deal but parties are frustrated that the delay in an agreement at Westminster could affect the chances of a deal in Northern Ireland.
DUP deputy leader Nigel Dodds told MPs on Wednesday evening that his party wants to see the Stormont Executive up and running as quickly as possible.
However, Colum Eastwood, leader of the Social Democratic and Labour Party (SDLP), claimed the "chaotic talks" between the DUP and the Conservatives were holding Northern Ireland politics to ransom.
"We're all, of course, a bit preoccupied by what's going on - or not going on - in London and it's quite clear that the DUP and Tory Party aren't quite sure what they're doing, but they need to get on with it, because it is affecting the process here," Mr Eastwood said.
"If people think that anyone is going to sign a deal here without knowing what's coming from London, that doesn't make any sense at all, because what we're trying to do here is form a government - a government that will need a budget."
He added: "We can't be secure or clear about any of that until we see what's coming from London."
Sinn Féin sources are "equally unimpressed", the BBC has learned.
They point out that, despite the fact the government has imposed a Stormont deadline of next Thursday, ministers have spent most of the last 10 days in a bilateral negotiation with the DUP aimed at propping up Theresa May's administration.
Republicans sources told the BBC said the Northern Ireland Executive will not be re-established from Westminster, but as a result of negotiations in Belfast.
They argued Stormont is where the focus of the government and the DUP should be.
There is a "very good" chance the Democratic Unionist Party (DUP) and Conservatives will agree a parliamentary deal by next week, a DUP MP has said.