McGhee's Motherwell side failed to make the top six in this season's SPL
Motherwell boss Mark McGhee has been recommended by departing Celtic manager Gordon Strachan as his replacement at Parkhead, BBC Sport understands.
Strachan stepped down in the wake of his failure to win a fourth successive Scottish Premier League title.
McGhee is also among the favourites to land the vacancy at Aberdeen.
"At the moment I've heard nothing but speculation and I can only say that it is a compliment to be linked with these jobs," McGhee told BBC Radio Scotland.
Bookmakers have West Brom manager Tony Mowbray down as favourite for the post at Celtic Park.
Mowbray, a former Celtic defender, impressed fans at the Hawthorns, despite the club being relegated from the Premier League in England this season - and also at former club Hibernian because of his attacking brand of football.
Celtic chairman John Reid hailed Strachan's "great professionalism, character and determination" and vowed to find a replacement to reclaim the top spot in the SPL.
"We will aim to appoint our new manager as soon as possible," said Reid.
"Our aim is to regain the championship and restore our pre-eminent place in Scottish football."
Burnley manager Owen Coyle's stock has risen considerably following his remarkable spell at the club.
The Clarets clinched promotion to the Premier League on Monday with a 1-0 win over Sheffield United in the play-off final.
However, he distanced himself from a move to Celtic Park.
"I didn't know there was a vacancy at Celtic," he said. "It's flattering that people mention your name, but I'm with Burnley.
"I'll concentrate my job on what I am doing here - and long may that continue."
McGhee, who spent four years playing for Celtic in the 1980s - following a six-year stint with Aberdeen, has long been touted as a candidate, although his Motherwell side could not repeat last season's feat of European qualification and missed out on the top six this term.
Former Hearts and Leicester boss Craig Levein is also highly regarded for the job he has done with Dundee United.
Wolves manager Mick McCarthy and Everton boss David Moyes are also former Celtic players who have done impressive jobs in England, although both are unlikely to leave the English top flight.
Strachan's successor will have a hard act to follow since he was the first Celtic manager to clinch a hat-trick of titles since Jock Stein, despite having significantly less money to spend than acclaimed predecessor Martin O'Neill.
And the club's summer transfer budget will be further hit by the lack of guaranteed Champions League football next term.
Rangers secured a place in the group stages and the £10m bounty that comes with it when they took the Scottish Premier League title, but Celtic must negotiate two qualifying rounds to join them.
Main shareholder at Celtic Park Dermot Desmond recognised Strachan's part in reducing the club's debt and wage bill.
"Gordon leaves Celtic a better club both on and off the balance sheet," stated the Irish businessman.
"Personally, I am extremely grateful for his contribution to the development of this great club."
McGhee, who played for Celtic in the 1980s, is a close friend of Strachan
Meanwhile, Rangers boss Walter Smith has paid tribute to the departing Strachan, who is thought to be on a three-man shortlist for the managerial vacancy at Sunderland and would be interested in a return to England's top-flight.
"I've been on record as saying that I find it very difficult the criticism that Gordon takes," said the Ibrox manager.
"A football manager has to be successful and I think Celtic have been extremely successful, not just in domestic circumstances but also in European games.
"I don't think that Scottish teams in recent years have had the credit for how they do.
"Rangers and Celtic get criticised for their European performances but we don't compete on the same field as a lot of the teams who are involved in the Champions League financially.
"We do so domestically and when we win the league, people make allowances for all the other clubs who can't challenge us.
"But they don't make allowances for us when we are unable to challenge in the Champions League.
"I think Gordon Strachan has done an excellent job at Celtic over the last few years."
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