Neil Lennon believes his former team-mate would be a success in the Parkhead hot-seat.
But it has emerged the Parkhead club would have to wait until November to land their No.1 target as Larsson has made a pledge to his current club, Falkenberg, not to leave before the end of the Swedish season.
Falkenberg officials have revealed there has been an approach directly to Larsson from an unnamed club.
But they have been assured he is not about to walk out, having only taken over in December.
All of which is bad news for Celtic, who could now switch attention to other names on their list of possible managers.
They could also attempt to put in place a temporary management structure - with a Director of Football position created - until they get their man.
Larsson would be a popular appointment with the majority of Celtic fans to whom he remains a club icon.
Lennon has vowed to help with the appointment of his successor if the club ask his opinion.
He says he understands why the bookies have made Larsson favourite to take over from him.
The outgoing boss - who was on the club's official charter to Lisbon yesterday ahead of tonight's Champions League final between Atletico and Real Madrid - said: "If he wants the job, I'm sure he will be a huge success.
"Why not? He's had a fabulous career as a player, he is a very intelligent guy and knows the game very, very well."
Those are qualities which have attracted the Celtic board, but which also make Falkenberg keen to keep him.
Their sporting director Hakan Nilsson, revealed: "Henrik is an honest person. He said he has had contact from a club.
"The only thing I know is Henrik is staying with Falkenberg this season. He said that to me."
Nilsson added: "I know him as a man of his word. We have no concerns about him leaving.
"I have no problem with the club who has spoken to Henrik.
"He had said no [to the approach], therefore it is no question for us."
Falkenberg have not closed the door entirely, however. Nilsson added: "If that offer comes, we will consider it. But we're very happy to have Henrik with us.
"He has a contract,
and that contract is between us and Henrik, no-one else."
Meanwhile, Celtic have confirmed they will play a pre-season friendly against St Pauli, in Hamburg on Saturday, July 26.
The game will come between the first and second qualifying rounds for the Champions League.
The Scottish champions will return to the Millerntorplatz Stadium for the first time since 2010, when they won 2-0 in a game played to mark the German club's centenary.