Jay would be a controversial appointment because she has close ties to the Labour Party. The government would be heavily criticised by the press if the BBC chairman and the director general were Labour supporters. Director general Greg Dyke was a donor to Labour before he took the helm at the corporation.
Baroness Jay has been joined in the race by Michael Grade, the former chief executive of Channel 4 and the man dubbed "pornographer-in-chief" by the Daily Mail.
Grade has surprised the industry by applying for the job, because only recently he said that although he would like the job it was unlikely he would get it. He said that there were two certainties in his life, "One is that I would like to be the chairman of the BBC. The second is that no one will ever ask me."
Grade formerly worked for the BBC as controller of BBC 1. He left when he fell out with the then director general Sir John Birt. However, Grade is believed to be one of Greg Dyke's preferred candidates for the £77,950-a-year part-time job.
Gavyn Davies, the current deputy chairman, is also believed to be a strong contender. However, his close ties with the Labour Party -- his wife Sue Nye works for Gordon Brown -- would likely work against him.
Davies is chief economist at Goldman Sachs and chaired an inquiry into BBC funding.
Other candidates include: Lord Burns, the former Treasury civil servant appointed by the government to sort out the National Lottery franchise debacle; and James Lee, chairman of Scottish Screen.
The new chairman of the BBC will be appointed by Tony Blair and culture secretary Tessa Jowell after an independent panel conducts the selection process. A decision is expected in the next few weeks.