Smith is understood to have held talks with Wolves owner Steve Morgan and chief executive Jez Moxey about taking the post until the end of the season after emerging as the favourite to step into the breach
The 63-year-old has been out of football since ending his second spell in charge of Rangers at the end of last season but has declined the opportunity to return to management in the Barclays Premier League.
It was earlier reported Smith turned down the Wolves job on a full-time basis but was happy to assume initial command for 13 games in a bid to keep Wolves in the top flight. However, he has now turned down the opportunity, leaving the Molineux outfit still to fill the breach.
Several bookmakers had made Smith the clear favourite to take over from McCarthy, who was sacked 11 days ago.
Wolves have endured a fruitless search in the past few days with Alan Curbishley, Reading's Brian McDermott and Brighton's Gus Poyet all rejecting their interest.
Former Sunderland boss Steve Bruce appeared to be the favourite after being interviewed last week, but Smith then moved into pole position and Wolves had even been hopeful of him being in place for Saturday's clash at Newcastle.
Smith has previous experience of managing in the Premier League during four years at Everton and was briefly Sir Alex Ferguson's assistant at Manchester United at the end of the 2003-04 season.
He was also manager of Scotland for two years before returning to Ibrox in 2007 for the second time when he led the Glasgow club to three successive titles and the 2008 UEFA Cup final.
Curbishley rejected the chance to replace McCarthy for a second time on Tuesday after initially being interviewed last week, while McDermott signed a new three-and-a-half-year contract with Reading on Wednesday. Poyet has confirmed Wolves' interest but is happy to remain at Brighton for the foreseeable future
Source: PA
Source: PA