Sources close to Mr Donaldson, the party’s current Westminster leader, have said he is highly likely to enter the race to succeed the deposed Arlene Foster, with an announcement anticipated later on Monday.
The North’s Agriculture Minister Edwin Poots announced his candidature last week.
If Lagan Valley MP Mr Donaldson throws his hat in the ring it will result in the first leadership contest in the party’s 50-year history.
Mr Donaldson is seen as the moderate candidate against the more hard line Mr Poots, who also represents the Lagan Valley constituency, as an Assembly member.
Mrs Foster resigned last week after an internal revolt against her leadership. The move came in the form of a letter of no confidence signed by a majority of the party’s senior elected representatives.
Mr Poots, understood to have been one of the key figures behind the heave against her, announced his leadership bid within 24 hours of Mrs Foster’s resignation statement.
The outgoing DUP leader will step down from that role on May 28th, and as the North’s First Minister at the end of June.
A small electorate, comprising just the party’s MLAs and MPs, will decide the leadership contest.
If Mr Donaldson does confirm his challenge on Monday it will coincide with the date viewed by many historians as the centenary of the creation of Northern Ireland.
On Sunday it emerged that Mr Poots would not take on the First Minister’s job if he was elected DUP leader, instead appointing an Assembly colleague to the role as he concentrates on the leadership.
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If Mr Donaldson won the leadership and remained as an MP at Westminster he would not be able take up the First Minister’s job.
Discontent at the DUP’s Brexit strategy was a major factor in the move against Mrs Foster, with party rank-and-file laying some of the blame for the emergence of an Irish Sea border at her door.
Traditionalists from the party’s religious fundamentalist wing also harboured concerns over positions Mrs Foster has taken on some social issues, in particular her decision to abstain in a recent Assembly vote on a proposed ban on gay conversion therapy – a proposal the majority of her party colleagues opposed.