If the results are reflected by votes cast at the ballot box next week, it will be the first time that a nationalist party is the largest at Stormont.
That would allow Sinn Fein to nominate the next First Minister, likely to be their vice president Michelle O’Neill.
At the last Assembly election in 2017, the DUP attracted 28% of first-preference votes and returned 28 MLAs, ahead of Sinn Fein who then received 27% of first-preference votes and returned 27 MLAs.
Support for Sinn Fein is now at 26% with the DUP on 20%, according to the latest the LucidTalk poll commissioned by the Belfast Telegraph.
Sir Jeffrey told the PA news agency he believes the DUP is going to win this election.
“I think the polls are not reflective of what I find on the doors in Northern Ireland,” he said.
“As we’re going around, there is strong support for the DUP, most unionists recognise the DUP is the only unionist party that can win, they don’t want to see Sinn Fein winning and taking forward their divisive border poll agenda.
I'm not bothered by polls and I think the political pundits who stake their reputation on the results of polls might get a surprise on May 5
Sir Jeffrey Donaldson
“Most unionists recognise there is a clear choice in this election, the DUP’s five-point plan or Sinn Fein’s divisive border poll plan and I think on May 5 we’re going to see unionists voting for the DUP and transferring their votes to other unionist parties because not only do I want the DUP to win, I want to see unionism win more seats as well and that’s entirely possible in a number of constituencies.
“I’m not bothered by polls and I think the political pundits who stake their reputation on the results of polls might get a surprise on May 5.”
The Lucidtalk poll puts the Alliance Party and the UUP on 14% each, the SDLP on 10%, TUV on 9%, Green Party on 3%, People Before Profit on 2% and others and independents on 2%.
TUV East Belfast candidate John Ross said he believes the poll “underestimates the scale of the TUV surge”.
He also blasted the party’s exclusion from TV leaders’ debates.
The TUV had one MLA in the last mandate but are targeting gains in this election.
“In excluding TUV from the leaders’ debates broadcasters are, Canute-like, seeking to stop the tide. They, like he, will fail,” Mr Ross said.
The Lucidtalk poll was carried out online on April 22-24 using its established online opinion panel, comprising of 13,816 members, which it states is balanced to be demographically representative of Northern Ireland.
The latest poll results were based on 3,699 full responses which were authenticated, audited and weighted to a NI-representative data-set of 1,708 responses which was used for analysis in terms of the final results.
Lucidtalk say all results are accurate in terms of being Northern Ireland representative to within an error of plus or minus 2.3% at 95% confidence.