The star of The Apprentice had been spotted at Downing Street last week
Sir Alan Sugar's appointment to a government job should not create a conflict of interest with his role in The Apprentice, MPs have been told.
The Tories have complained that his new role as enterprise tsar is "completely incompatible" with BBC rules.
The new Culture Secretary Ben Bradshaw, a former BBC reporter, said it was up to the BBC but he did not think there would be a problem.
Sir Alan says he considers the advisory role to be "politically neutral".
Mr Bradshaw was appointed as culture secretary in Friday's reshuffle, which also saw Sir Alan accept a job as enterprise tsar - which he described as helping businesses and entrepreneurs.
In his first Commons appearance in his new role, Mr Bradshaw was challenged about Sir Alan's appointment by his Tory shadow Jeremy Hunt.
Mr Hunt asked: "Do you believe that Sir Alan Sugar can combine his role as host of Britain's most popular business TV programme with his new job as the government's enterprise champion, where he will sit in the House of Lords taking the Labour whip?"
Would it be right for the BBC to carry on screening The Apprentice when its main star is a principal advocate of government business policy?
Jeremy Hunt Conservatives
He has written to the BBC Trust to demand that Sir Alan choose either to stay in The Apprentice - or take the enterprise job.
Mr Bradshaw replied that he would be "interested to see a copy of the reply".
He added: "On the face of it, I don't see there is a conflict of interest here. From my memory of the BBC producer guidelines they were very clear about people who were involved in political programming not doing political jobs.
"But I seem to recall [shadow business secretary] Ken Clarke presenting a jazz programme in the past and there was no suggestion there was a conflict of interest there."
But he said it was a "matter for the BBC" and he understood Sir Alan had discussed it with them beforehand.
However Mr Hunt said it was "something quite unprecedented where someone has their own weekly TV programme at the same time as being one of the main ambassadors for government policy in precisely the same area."
He said, were an election held in June next year, The Apprentice would go out during the campaign.
Sir Alan: "I'll act as a kind of giant Dragons Den"
"In that period would it be right for the BBC to carry on screening The Apprentice when its main star is a principal advocate of government business policy?"
Mr Bradshaw said it was an issue for the broadcaster and he would await the BBC's response.
Mr Hunt has since published a letter he sent to BBC director general Mark Thompson asking whether rules relating to MPs and MEPs would also relate to Sir Alan, if he took the Labour Whip in the House of Lords.
"Specifically, if he becomes a Labour Peer, I wondered whether an assessment has been made as to whether you would need to reschedule the next series of the Apprentice to take into account the need for impartiality during a general election?," he wrote.
Asked about the issue on Sunday, Sir Alan told the BBC: "I wouldn't join the government, I don't see this as a political thing."
He said he made it "perfectly clear" to Mr Brown that he would not compromise his position on The Apprentice - the BBC show that Sir Alan fronts.
A spokesman for the BBC Trust said would respond shortly shortly to Mr Hunt.
A BBC spokesman said: "Sir Alan is in discussions with us about his plans and has assured us that he is determined not to do anything that would jeopardise his work at the BBC, which is something he greatly values."
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