Former boss, Neil Lennon, who quit last week believes his former team-mate would be a success in the Parkhead hot-seat. Lennon has already vowed to help with the appointment of his successor if the club ask his opinion.
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.
Falkenberg's 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."
Larsson remains the bookies favourite despite the difficultes.