Nicola Sturgeon believes Celtic have questions to answer over their Dubai trip.
The First Minister feels some photographs she has seen from Celtic's training camp suggest the squad might not be complying with social-distancing guidelines.
Celtic insisted on Monday that they had received Scottish Government approval for their mid-season trip following criticism of the timing of their excursion, two days before Scotland went into lockdown from already strict restrictions.
Travel, even within Scotland, is only permitted for "essential reasons" and the Scottish Government asked the Scottish Football Association to investigate the matter on Monday.
Speaking at her media briefing on Tuesday, Sturgeon said: "As I understand it, the Scottish Government gave some advice to the SFA about the rules around elite training camps back in November last year. The world around the pandemic has changed quite a bit since November.
"It's not our role to sign off or agree or not agree on what a football club does in terms of training camps. We set out what the rules are.
"The rules have been – and they may need to change given the changing nature of the pandemic – that elite sports can go overseas for training camps if that's important in the context of their training for competitions.
"For me, the question for Celtic – and I am trying to be diplomatic here – is not so much 'are they overseas at a training camp?'. It may be given changing circumstances that in future that won't be appropriate.
"But that's not really the question. It's 'what is the purpose of them being there?'
"I've seen a comment from the club that said it's more for R and R than it is for training.
"I have also seen some photographs – and I can only comment on what I have seen, I don't know the full circumstances – that would raise a question in my mind about whether all the rules at what elite players have to do in their bubble around social distancing are being complied with.
"So I think there are things there that should be looked into.
"Elite sport, and this is not just about Celtic or football, has been in a privileged position at many points over the past year, doing things that the general public can't do.
"We all want our sports teams and people to do well and be able to train properly, but as long as that's the case it's really important that they don't abuse it, that they use it for the purpose it's intended.
"And that applies to Celtic as it would to anybody else in that position."
Celtic posted a series of tweets on Monday evening, maintaining that they had not breached the rules.
The club said: "The training camp was arranged a number of months ago & approved by all relevant footballing authorities & @scotgov through the Joint Response Group on 12th November 2020.
"The team travelled prior to any new lockdown being in place, to a location exempt from travel restrictions.
"The camp, the same one as we have undertaken for a number of years, has been fully risk-assessed.
"If the club had not received Scottish Government approval then we would not have travelled."
Meanwhile, Glasgow Warriors assistant coach Kenny Murray is preparing for cross-border games to resume after Friday's Guinness PRO14 clash with Edinburgh.
Both Scottish clubs face Heineken Champions Cup trips to France this month as well as hosting English opposition.
Murray said: "As far as we are concerned, after Edinburgh the next two European games will go ahead, and then after that we will play Treviso. And then there will be a couple of weeks' break and we will be back into PRO14 again. It's good that we can keep going."
The European Professional Club Rugby body held talks with unions on Monday with further updates expected soon but it stated that no clubs were intending not to fulfil their fixtures.
