Published Tuesday, 27 July 2010
Writing in the News Letter, the former First Minister warned that such a move would only benefit those want to have senior positions at Stormont.
"Limiting that choice is not in the interests of the province but merely in the interests of those who want power," Lord Bannside told the News Letter.
During a speech before the Twelfth, the Orange Order Grand Master Robert Saulters hinted that he would like to see moves towards unionist unity.
Dr Paisley - who earlier this month entered the House of Lords - also said he would have to accept the will of the people of Northern Ireland if Sinn Fein ever took the First Minister's post.
"For many years I had to accept that the Democratic Unionist Party that I founded and led was not the majority party.
"Sinn Fein didn't become the majority party on my watch.
"Naturally, as a unionist, I will continue to play my part to prevent that happening in the future," he said.
Lord Bannside added that unionist unity is a good thing for the UK as a whole.
"Unionist unity - in its broadest sense within Great Britain - is essential for the health of the nation.
"A unified sense of loyalty to the throne and to the constitution ought to be top of the agenda with each of the devolved institutions," he said.
"Within Northern Ireland, unionist unity in the sense of one grand political party is, in my opinion, a non-runner."
Leader of the Traditional Unionist Voice party, Jim Allister, who has been highly critical of the DUP political strategy, has criticised Lord Bannside's remarks.
"It must never be forgotten that part of the Paisley legacy is the very prospect of a Sinn Fein First Minister, because it was his and the DUP's connivance at the legislative change in the St Andrews Bill which made it possible, " he said.
"The other striking feature of Ian Paisley's contribution in today's News Letter is the obvious discord with the present DUP leadership, epitomised by his jibe about how things were different on his watch."