The vultures are circling, and the first attempts to pick off the club's prize assets have already been made with Southampton making an offer for the keeper and Sunderland preparing their bid for the central defender.
Celtic remain in the driving seat, having both men under contract for another couple of years, and holding a strong financial position because of how well their business has been conducted in the past few years.
Neither Fraser nor Virgil appears to be agitating for a move away from Celtic Park, and that is also a plus.
But, of course, every player has his price. What Celtic are determined to do is ensure that is paid before they will even contemplate letting one of their top men go.
They followed this solid strategy when they sold Aiden McGeady, and again when Victor Wanyama was allowed to move.
The result was over £22million brought in, massive money for two players who cost less than £1m between them.
What is Fraser worth? Celtic will have their figure in mind, but, wisely, will not be prepared to make it public.
If I was the man valuing him, I'd say it should be £8-10m. That might seem low for someone who was in England's squad for the World Cup finals as the other 22 who travelled would all be priced higher.
But, it is a consequence of the league Fraser is playing in.
Whether you think that's fair or not, the fact remains players based in other leagues, especially the English Premier League or even Championship, are valued higher because there is so much more money swilling around there.
The other thing you have to take into account is that keepers are never valued as highly as outfield players, especially goalscorers.
Real Madrid have just paid £63m for James Rodriquez, while Barcelona paid £75m for Luis Suarez, who were both among the goals at the World Cup.
But, if Germany's keeper, Manuel Neuer, was sold tomorrow, he would not go for anything like that - and no-one proved their worth more than him at the World Cup.
I believe I am right in saying only a handful of keepers in the world have ever moved for more than £10m.
I know Craig Gordon was sold to Sunderland for £9m back in 2007, but that was an exceptional bit of business by Hearts at that time, and not an accurate yardstick.
I am not sure that Fraser will be desperate to go. But, I am sure that, having spent over a month with 22 players based in England during the World Cup build-up and finals, he will know what is on offer down south.
What he has to weigh up is what playing for Celtic is worth to him, not just in terms of wages, but experience and exposure.
Without playing on the Champions League stage - which he would not have got playing as back-up or even third-choice keeper at a club in the Premiership - would he have made it into Roy Hodgson's squad for Brazil? Unlikely.
Now, though, he might be thinking he has to be playing every week across the border to challenge for the No.1 place in the England team.
Celtic reaching the Group Stage of the Champions League will be a big factor in how he views his future, so the next few weeks are going to be very important as the window does not close until after the play-offs have been completed.
His performances in these big European games are what have made his reputation, but it is also what has made him so sellable.
Virgil is slightly different as he has had only one season at the club and has not established himself to the same extent in the Champions League, where Celtic players are really measured.
I still believe he would benefit greatly from another year here. He is only 23, so there's no clock ticking for him.
My only worry is that Virgil may already believe he has achieved all he can at Celtic. Certainly, his body language suggests he is finding it all a bit too easy. His agent also seems to be happy to talk about him moving, which is never a good sign.
Virgil could also be looking at the fact Louis van Gaal - who never selected him - has stepped down as manager of the Dutch national team, and the door may be opening for him to break through to that squad.
But, he should remember Fraser managed to make the international step-up while at Celtic by working as hard as he possibly could and giving his all in every match.
The likes of Southampton and Sunderland may not seem like the most attractive clubs Fraser and Virgil could get. But, as a player, you can only go where someone wants you - and where they have the money to make it happen.
Neither Southampton nor Sunderland are as big a club as Celtic.
But what both have going for them is that they play in the most lucrative league in the world.