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DUP First Minister Paul Givan and Agriculture Minister Edwin Poots have both said they intend to stand in the next Northern Ireland Assembly poll.
This could mean all three men will run for the DUP in the Lagan Valley constituency, where it currently holds two out of five seats.
The party lost its third seat in the last Stormont election in 2017.
Sir Jeffrey is currently an MP at Westminster.
However he intends to become first minister of Northern Ireland if the DUP wins the election - due in May 2022 - and he needs to be a member of the assembly (MLA) to do so.
Mr Givan and Mr Poots currently represent Lagan Valley in the assembly.
Mr Givan said it would depend on discussions with the constituency association but said it was his preference to remain at Stormont.
Speaking on the BBC's Good Morning Ulster programme, Mr Poots said: "I don't know what the future holds and I don't believe in speculating but at this moment in time I intend to carry out this role until the next election and stand in the next election, that is most likely my intention and in the meantime, we'll take things from there.
"I was never a career politician so politics has happened for me. I could live outside of politics but at this moment in time, it is not my intention to leave politics. It is my intention to continue.
"I need to reflect on what my constituency are saying to me and the feeling that I am getting is that my constituency want me to stay on and do the job and I will work with them on that."
If Sir Jeffrey was elected as an MLA he would have to step down as an MP, which would lead to a Westminster by-election
Mr Poots said he "wouldn't rule out" standing in a by-election if that happened.
"I have no preference, I'm very relaxed about it," he said.
"I have been in politics since 1996 and I've had a pretty long career so I will take whatever challenges 2022 brings to me and face them head on.
"I wouldn't rule that [Westminster] out but I've always enjoyed being up at Stormont.
"These are all things we need to sit down and have a conversations about going forward. I want to see the DUP do well for the benefit of unionism and the benefit of the wider public in Northern Ireland."
Strategy
On Wednesday afternoon, Mr Givan said Mr Poots would have his "full support" if he decided to make a bid to become an MP.
"He has served the people of Lagan Valley for over 25 years and has vast experience he gained locally, that would give him clear strengths to represent Lagan Valley at a national level," he told BBC News NI.
Mr Givan, who has been an MLA since 2010, said internal discussions would take place to decide how best to "maximise the number of candidates we're going to run" in Lagan Valley.
"It's been a privilege for me to serve the people of Lagan Valley and I've every intention to continue doing that," he added.
Mr Poots initially defeated Sir Jeffrey in the DUP's first ever leadership contest earlier in the year.
However, he was forced to resign within weeks following an internal party revolt over his decision to proceed with the appointment of Mr Givan as first minister.
Sir Jeffrey then stood again for party leader and was elected unopposed.
At the time, he said he intended to return to Stormont from his current position at Westminster.
Until Tuesday, Sir Jeffrey had not declared which constituency he intended to stand in.