"Several" Ulster Unionist Party members have urged Robert McCartney to challenge for the leadership of the UUP, the UK Unionist Party leader has claimed.
Mr McCartney indicated that with the right approach he might be persuaded to stand.
While some Ulster Unionist MLAs are dismissive of the prospect of Mr McCartney being appointed leader, he said he had several approaches over the past three weeks.
He said the approaches were obviously "detonated" by Lord Kilclooney's recent description of the leadership contenders as "has beens" and his suggestion that the UUP should look outside the party for a new leader.
The 800-member Ulster Unionist Council (UUC) is due to elect the new leader on Friday week.
Three Assembly members have declared for the position; Sir Reg Empey, David McNarry and Alan McFarland. Former UUP MP Sir Ken Maginnis is deliberating whether to run.
Mr McCartney said he would not rejoin the UUP so that he could out stand for election at the UUC gathering on Friday.
"But if the people decide that none of the candidates are satisfactory and then issue some invitation to me - which I think is unlikely - then that would be the time to consider what this is all about."
Mr McFarland said Mr McCartney had "fallen out" with too many unionist colleagues to be now seen as the party saviour.
Mr McFarland has garnered support from the party's only MP, Lady Sylvia Hermon and MLAs Lesley Cree and Esmond Birnie.
MLA Billy Bell, who attended Sir Reg's launch last week, was also present at Mr McFarland's launch. He said he has yet to decide which of the candidates he will support.
While some pundits see Sir Reg as favourite to win on Friday week, Mr McFarland believes a "grassroots rebellion" will return him as the next UUP leader.
He said he would be well capable of facing up to senior DUP politicians such as Peter Robinson and Nigel Dodds.
"For those who know me will know I have an iron willDon't mistake me having good manners and being well brought up for someone who cannot lay you out if, in fact, that's required."