Forest are looking to appoint a new manager after the Kuwaiti-based Al-Hasawi family, who took charge at the City Ground a week ago, sacked Steve Cotterill last Thursday. Former Forest midfielder Keane was immediately installed as one of the favourites to replace Cotterill.
Solicitor Michael Kennedy, who represents the 40-year-old, says Keane would be interested in ending his 18-month exile from management to talk to the club he served for three years as a player in the early 1990s.
"As far as I know, he has not been approached and he has not applied for the job. But I haven't spoken to him about it so I wouldn't know for sure," Kennedy told Press Association Sport.
"I can understand why people would link him with the job, being an old Forest player, but I don't know if he is in the running for it.
"I thought it was Mick McCarthy until Monday. Or perhaps Glenn Hoddle, according to some reports. But what I can say is that I think Roy would be interested if he was approached. He is available and I think it would be a job that would appeal to him."