The club's new Kuwaiti owners had confirmed that McCarthy cut short a holiday to enter talks over taking the manager's job, but widespread media reports said the Irishman had withdrawn from the running.
The Al-Hasawi family said that the former Wolverhampton Wanderers, Sunderland and Republic of Ireland boss was one of several candidates on the shortlist for the job at the City Ground, made vacant last week when previous manager Steve Cotterill was sacked shortly after the takeover was completed.
"Mick is one of the people we are talking to, but there are others," said Abdulaziz Al-Hasawi earlier on Monday. "If he meets our requirements, we would be honoured to work with Mick.
"It is very important for the manager to have good knowledge of this league and the teams involved in it. They must also have an understanding when it comes to working with a club and developing it."
McCarthy has been out of work since he was sacked by Wolves in February,
Other candidates for the job are thought to include Peterborough boss Darren Ferguson, former Ipswich Town manager Roy Keane and former Notts County director of football Sven-Goran Eriksson.
"We are looking for somebody with a strong CV, with a lot of experience," Al-Hasawi added. "We want somebody who has good, strong character to come in and inspire the players.
"We have interviewed some people on the phone but we're starting to see people face to face and you get a much better impression when you see them face to face. They are more comfortable and can speak more openly."
Forest's owners are hopeful of announcing their new manager by the end of the week.