However, he refused to confirm if any of his party colleagues would also attempt to avail of the dual mandate.
Four of the five parties that make up the Executive in Stormont have come out against the plans by the Northern Ireland Office.
SDLP MP Claire Hanna said the proposals were a “safety net” for Sir Jeffrey, while Ulster Unionist leader Doug Beattie referred to them as a “scam”.
The return of the “dual mandate”, or double-jobbing, would allow the DUP leader to contest the forthcoming Assembly elections while also remaining MP for Lagan Valley at Westminster.
The UK Government plan would see dual mandates returning only until the next UK general election in 2024.
The current law banning politicians from double-jobbing as MLAs and MPs came into effect in 2016.
Sir Jeffrey told the BBC Good Morning Ulster programme: “There is no agreement on this between the DUP and the Government, we are very clear where we stand on a range of issues.”
He said: “If this legislation is passed by Parliament, it will be available to any Member of Parliament in Northern Ireland who wants to switch back to the Assembly; it is up to each individual MP.
“If this legislation is approved then I will consider whether I can avail of this option.”
The DUP leader added: “I think there is a case to be made at this particular time in the current circumstances of Northern Ireland. It is important for unionism to have a strong voice in the Parliament of the United Kingdom.
“It will be the people who decide this. If I am selected as a DUP candidate and I stand in the Assembly election, and if Parliament approves this proposal, it will be for the people to decide whether or not they think this is a good thing.”
Amid reports that a second DUP MP is seeking to secure a Stormont seat, Sir Jeffrey refused to confirm whether any of his party colleagues had put their names forward for the Assembly elections later this year.
He said: “The bulk of DUP MPs have not put their name forward for selection.
“I see some parties saying that all eight DUP MPs will be standing in the Assembly elections – that simply is not true.”
Sir Jeffrey added: “Even before I was elected leader of the DUP, last year it was the Labour Party, the sister party of the SDLP, who first put this (amendment) forward.
“Furthermore, it was then put forward as a proposal when the NDNA (New Decade, New Approach) Bill was being debated in the House of Lords.
“I have had a look at that debate and I note that none of the parties who are objecting now raised an objection at that time.”
But Ms Hanna responded: “Jeffrey Donaldson can put up all the straw men that he wants, it is quite clear that the other parties don’t support this because it reduces the function of elected representatives.
“These two parliaments run at the same time. You can’t do justice to both roles and you are not doing justice to your elected representatives.
“What is concerning people is the fact that this feels very much like a stroke, and it is a stroke to benefit Jeffrey Donaldson.
“The reason Jeffrey Donaldson wants this safety net is because he is dangling the future of the (Stormont) institutions by a thread.”
Mr Beattie told the BBC Nolan Show: “You cannot do two full-time jobs at the same level as you can do one, that is a simple fact.
“This was brought in so close to an election only to benefit one party and that makes it a scam.”
At the weekend, Sinn Fein deputy First Minister Michelle O’Neill labelled the Government plans a “disgraceful interference in the upcoming Assembly election”.
A spokesman for the Northern Ireland Office confirmed the Government had tabled an amendment to the NI (Ministers, Elections and Petitions of Concern) Bill and said it would be subject to the usual parliamentary scrutiny.