Scottish Football Association chief executive Ian Maxwell believes Celtic may be considering the impact of their trip to Dubai in the wake of their Covid-19 fall-out.
The Parkhead club had one player test positive following their return to Scotland from their regular mid-season training camp on Friday.
However, boss Neil Lennon, assistant John Kennedy and 13 first-team players have been deemed to be closed contacts of the infected player - revealed to be defender Christopher Jullien - and have gone into self-isolation.
Maxwell was at pains to stress that Celtic were given approval by the Scottish Government for the trip through the elite athlete exemption.
"It is not our permission to give," he said, before adding: "They now find themselves in a position which they would not want to be in under any circumstances in terms of the positive case, the number of close contracts identified.
"It is fair to say that if Celtic had been at home they would still potentially have had one positive case but it would have been one player missing.
"And that is the danger of travelling abroad, there is a lot more inherent risk involved from a close contact perspective because of the travel on planes and buses.
"So from that perspective, I am sure Celtic are revisiting the requirement to go and the decision that they made to go, and that is something for them to reflect on, given the fall-out there has been."
Maxwell was speaking on a day that it was announced by the SFA board that, in the interests of public health and with an increase of Covid cases across the country, football below Championship level would be suspended for three weeks at midnight.
The suspension of the game below the top two tiers will last until January 31, and will be reviewed on a rolling basis by the Scottish FA board in partnership with Scottish Government.
The William Hill Scottish Cup will also be suspended, with any matches due to be played prior to February 1 to be rescheduled.
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Neville was approached about the role before the departure of Diego Alonso was confirmed and it is understood he has now agreed terms. The move will effectively rule him out of guiding the Great Britain women's football team at this year's Olympics.