The person is one of seven to be rejected by the House of Lords Appointments Commission.
The commission does not reveal the names of those who were put forward or its reasons for turning them down.
But it has been revealed that the DUP declined to nominate a substitute when asked to do so.
In response to speculation that he was the person concerned, the former South Antrim MP William McCrea told the Irish News: "I haven't heard of it. I really haven't a clue."
But the BBC understands the DUP's intention is to nominate the former MP, who lost his seat is May, for the House of Lords in the next round of nominations.
Of the other names blocked by the commission, five were nominated by the Conservative party.
The sixth is the former Liberal Democrat minister David Laws who resigned over an expenses scandal in 2010.
A Democratic Unionist Party (DUP) nominee for a peerage has been blocked by a parliamentary watchdog.