DUP deputy leader Nigel Dodds was in line to succeed top Tory Liam Fox as international trade secretary until Theresa May vetoed the plan, according to press reports.
It is claimed that during the post-election negotiations between the DUP and Mrs May's government, former Tory chief whip Gavin Williamson secretly offered a cabinet seat to Arlene Foster's party in return for the support of her ten Westminster MPs.
Now defence secretary in Mrs May's cabinet, Mr Williamson is said to have gone "well beyond his mandate" in seeking a formal coalition deal with the DUP during June's protracted talks.
The former chief whip is thought to have been one of the most enthusiastic supporters of a deal with the DUP after June's election left the Tories without a Westminster majority.
Mr Williamson argued that without the DUP’s ten MPs Mrs May could not hope to run a successful minority government and was backed by Sir Jeremy Heywood, the cabinet secretary.
The negotiations with the unionists went on for almost two weeks, requiring the repeated postponement of a vote on the queen's speech.
A confidence and supply deal was eventually agreed that sees the DUP support the Tories on votes involving finance and Brexit.
In return, the DUP secured around £1 billion of money for health service reform, education and infrastructure in the north.
The party took no role in the cabinet but according to The Times, Mr Williamson had previously offered the party a place at the cabinet table.
"One afternoon fairly early on Gavin came back and it became apparent that instead of agreeing a confidence and supply deal he was offering a full coalition with the DUP, including a a full cabinet post," the paper quotes a former official saying.
According to the report, Nigel Dodds had been lined up to replace Liam Fox as international trade secretary in the putative coalition before Mrs May ordered her chief whip to withdraw the offer.
"We were pretty horrified," the source told the newspaper.
He was told to take it off the table pretty sharpish."
According to the same report, a spokesman for the defence secretary said; "This story is not true".
