Livingston boss Davie Hay has admitted he may have to consider any approach from Hibs to become their manager if no new owner can be found for Livi.
Berti Vogts thought that Burns was not interested
But Hay insists he would prefer to stay on at Almondvale if the club's future can be secured.
Celtic youth boss Tommy Burns is also understood to be interested in the vacant manager's role at Easter Road.
And BBC Sport understands that he would want Celtic captain and midfielder Paul Lambert as his assistant.
Hay told BBC Scotland's Sportscene that he was hopeful that a consortium, understood to be on the verge of being granted preferred bidder status for Livingston, would take the club out of administration.
But he admitted that if that did not happen, the option of a secure job elsewhere would become more attractive to him.
"I met one of the gentlemen (in the consortium) yesterday (Friday) briefly and it looks positive," he said.
"It means we might be able to talk to the players who are out of contract to try to keep the squad together and possibly even add to it. There might be some confirmation on that front early next week."
With regards to the Hibs job, he added: "It's Hibs' decision who they go for. I'd like to wait and see if something positive happens here.
"But if it doesn't, I'd have to consider other options wherever they might come from."
Burns' prospects of taking over the reigns at Easter Road will be reduced by the need to compensate both Celtic and Scotland, for whom he is assistant.
Hibs may not be able to afford his services, having already reduced Williamson's salary by a third this season in an attempt to reduce the Edinburgh club's debt burden.
Scotland boss Berti Vogts had this week suggested that Burns would not be interested, but it appears that he would be attracted to a return to club management after spells in charge of Kilmarnock, Celtic and Reading.
Veteran Scotland international Lambert has been a bit-part player this season as Celtic have regained the Scottish title and has admitted that he will soon move into coaching.
Meanwhile, Hibs caretakers Jim Clark and Gerry McCabe look set to follow former boss Bobby Williamson to Plymouth Argyle.
Clark and McCabe, who take charge for the first time when Hibs visit Kilmarnock, have hinted that they are likely to join Williamson at Home Park when their contracts end in the summer.
Gerry McCabe and Jim Clark are likely to leave
McCabe said: "We will be speaking to him soon and take it from there.
"We will just have to wait and see, but whoever come in here will inherit a good squad of boys."
Clark added: "I am definitely not putting myself forward for the Hibs job.
"We've spoken to Bobby informally, but we've had no contact with Plymouth.
"Bobby will be concentrating on his game at the weekend and we'll be concentrating on the Hibs game.
"But the Hibs board have got to appoint someone as quickly as they can - it's only common sense."
Clyde player-boss Alan Kernaghan and Inverness Caledonian Thistle manager John Robertson have also been linked with the job.