The move is part of an attempt to diffuse a row that is brewing between the two political parties. The row centres on the fact that two of the three top posts at the BBC have now been filled by former Labour Party supporters in director general Greg Dyke and newly appointed chairman Gavyn Davies.
The Conservatives expressed anger about Gavyn Davies' appointment, which was announced on Wednesday.
Their complaints have come despite the fact that the last two chairmen, Sir Christopher Bland and Marmaduke Hussey, were Conservative supporters and selected by Downing Street.
This time round, candidates were interviewed by an independent panel and its recommendations were then passed on to the culture secretary Tessa Jowell and prime minister Tony Blair. Davies is said to have been such a strong candidate that his was the only name put forward.
A spokesman for Duncan Smith confirmed that he had been approached by Downing Street and that he does intend to put forward candidates.
One name which has been mooted this week is former Tory leadership challenger Michael Portillo. Outgoing BBC chairman Sir Christopher is said to have given Portillo strong encouragement.
In an interview on Radio 4's Today programme, Sir Christopher said, "[Portillo] is a man of considerable achievement and a high-quality potential candidate."
When asked whether Portillo would likely secure the position, Sir Christopher replied, "There is absolutely nothing to stop him."
Other Conservative names that have been linked to the position include Baroness Hogg, who was the head of John Major's policy unit between 1992 and 1995.
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