Smith, who was ousted from his position as culture secretary in the last cabinet reshuffle, is understood to have been informally approached about the position and is said to be enthusiastic.
However, because he is a Labour MP and a former member of the government, his appointment is almost certain to lead to accusations of cronyism. Ofcom is being set up as a politically independent organisation.
Last week, it was reported that Gavyn Davies, the deputy chairman of the BBC, had been sounded out about the job. He is said not to be interested.