East Antrim MP Mr Wilson said the current Lagan Valley MLA lost out to the best candidate – Diane Forsythe – and that it is “disappointing that Edwin has not accepted the decision”.
On Friday, DUP party officers selected Ms Forsythe ahead of Mr Poots, who was attempting to switch to the constituency from Lagan Valley.
That decision still has to be ratified at a meeting of the party’s executive next week, however, Mr Wilson said he sits on that, and that they will make the same decision again if the party’s ruling executive refers it back for a review.
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“As a party officer, I was amongst those who interviewed both candidates seeking the DUP nomination for South Down,” Mr Wilson said in a statement on Wednesday night.
“Diane was by far the best candidate. Her track record speaks for itself. She obtained the largest ever DUP vote in South Down when she contested the 2017 Westminster election.
“All across the constituency, her selection has been positively received. As someone who is well connected locally and is passionate about her home area, we were delighted to endorse a candidate of Diane’s calibre.
“Diane is both the party officers’ and the party leader’s choice for South Down. Even her political opponents have admitted that she is the best candidate the DUP could have put forward.”
Mr Wilson added: “It is disappointing that Edwin has not accepted the decision, especially because he has a seat of his own which he is free to contest and there are other vacant places available which he could have chosen and is still free to choose if he so wished.
“Any executive challenge would not result in Edwin replacing Diane as the candidate in South Down. The matter would simply be deferred to those officers and the leader, who have already expressed their view on who the best candidate is.”
Earlier on Wednesday, Mr Poots hit out at those within the DUP who had leaked the details of the internal party selection processes to the media.
He told the BBC Good Morning Ulster programme: “I am engaged in a process, an incomplete process, for nomination to stand for the Assembly.
“Some very silly people, some irresponsible people, thought that they would leak elements of that process to the press.
“It was a very stupid thing for them to do and I don’t intend to engage in talking about an internal party process which is incomplete.”
He added: “I think there was a little excitement over the weekend and people were writing off Edwin Poots’ political career and they were getting a little carried away with themselves.
“I can assure you that my demise has just happened quite yet, the obituary writers need to put their pens down. Edwin Poots hasn’t gone away.”