Scotland’s First Minister Nicola Sturgeon says Celtic have questions to answer about their trip to Dubai.
Ms Sturgeon says possible breaches of social distancing rules while in the Middle East “should be looked into”.
However, Celtic insist the training camp was approved by the Scottish government, while the Scottish FA have no plans to investigate the trip.
“For me, the question for Celtic is what is the purpose of them being there,” Ms Sturgeon said.
“I’ve seen comments from the club that it’s more for R&R than training.
“I have also seen some photographs – and I don’t know the full circumstances – that would raise a question in my mind about whether all the rules elite players have to follow in their bubble around social distancing are being complied with.”
Pictures have emerged of members of the Celtic party in the UAE not wearing face masks and potentially breaching the social distancing rules that those in Scottish football must adhere to.
It remains unclear if the Scottish FA will investigate that matter.
Celtic travelled to the United Arab Emirates on Saturday just hours after their 1-0 defeat by Rangers.
Travellers returning from the UAE are exempt from self-isolation protocols in Scotland, with elite athletes in Scotland permitted to travel abroad to compete.
“Elite sport has been in a privileged position and as long as that is the case it’s really important they don’t abuse it,” said Ms Sturgeon at her daily coronavirus briefing on Tuesday.
“I saw their [Celtic’s] statement and have not spent a lot of time looking into it, but as I understand it the government gave advice to the Scottish FA about the rules around training camps in November.
“The world has changed quite a bit since then but it’s not our role to sign off what a club does around these training camps.
“The rules may have to change, but they were that elite sportspeople and teams can go overseas if it is important in the context of training and competitions.”
Mainland Scotland has been in Tier 4 – the highest level of restrictions – since 26 December, and Ms Sturgeon addressed the nation on Monday ordering people to stay at home where possible.
Deputy first minister John Swinney has accused Celtic of not setting “a particularly great example”.
“I don’t think it’s a good idea,” he told BBC Radio Scotland on Monday.
“When we are asking members of the public to take on very, very significant restrictions on the way in which they live their lives, I think we have all got to demonstrate leadership on this particular question.”
When approached for comment on Monday, a Celtic spokesman told BBC Scotland: “The training camp was arranged a number of months ago and approved by all relevant footballing authorities and the Scottish government through the Joint Response Group on 12 November.
“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.”
In November, Celtic requested their fixture with Hibernian, originally scheduled for this weekend, be moved to Monday, 11 January to accommodate the trip.
The SPFL granted the change, despite objections from the Easter Road side.