Wilfried Nancy presided over training at Lennoxtown on Thursday amid social media rumours that the Celtic manager was facing a swift exit from his position.
Fans bluntly called for the Frenchman to leave at Tannadice on Wednesday during a fourth consecutive defeat in charge.
A Celtic source dismissed claims that Nancy was meeting with board members to discuss a severance package just two weeks after arriving in Glasgow.
The 48-year-old has overseen Celtic’s longest losing streak since 1978 and defeat to Aberdeen on Sunday would match a run not witnessed since the 1952-53 season.
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Defeat at Dundee United came shortly after Celtic chief executive Michael Nicholson declared the club’s backing for Nancy was “absolutely solid” and that transfer window planning was under way.
But the former Columbus Crew head coach faces a challenge to get to January unscathed with away games against Livingston and Motherwell also coming before the New Year derby against Rangers.
Celtic enjoyed their best period in a game under Nancy when they took the lead early on at Tannadice and created several good chances.
But United had already grown as an attacking force before half-time and two goals in three minutes around the hour mark came amid a period of sustained pressure from the home side.
Nancy’s analysis that his side played well and were punished for two set-pieces against the run of play did not match the stats, which showed United had 16 efforts at goal.
The game quickly followed news that Peter Lawwell was stepping down as chairman, citing “abuse and threats” from supporters.

Lawwell will be temporarily succeeded by long-serving director Brian Wilson from January 1st and the former Labour MP and UK government minister declared that change had been in the pipeline before Lawwell’s announcement.
Wilson told Celtic TV: “Celtic’s been part of my life since almost the day I was born, so I’m going to accept that [role].
“I accept that it’s going to come with its pressures, but I also want to get the message across that it is an interim role and what we’re trying to do is part of a process of change, a process of moving on and a refresh.
“And that was going to happen anyway, a strategic look at how we do things and hopefully the problems which everyone recognises have arisen in recent times, that they can be addressed.”
The 77-year-old added: “One of the few benefits of advancing ages, you can remember times before where Celtic were in tough corners but came through and came through stronger.
“Sometimes it took a lot longer than I hope it’s going to this time, but the immediate thing is that we win games and we have a successful season.
“It’s not as successful as we wanted it to be when we started it, but it can still be a successful season.
“But that does depend on unity, it does depend on the supporters continuing to get behind the team because our objective this season is to win the league, to win the Scottish Cup, to do well in Europe and all of that is perfectly feasible.
“But we’ll only do it if we’re united and surely that is possible, surely that’s what 99 per cent of Celtic supporters want?
“Just give us a chance to do this and to do it properly, to have transition, to have a refreshment of the approach, to recognise where there’s weaknesses, to build strength and to go forward together.”














