The Nigerian is being targeted by Premier League new boys, Burnley. And his sale would almost certainly mean no-go for the Dutchman
Clarets boss, Sean Dyche, is in the market to strengthen his side, and has already recruited six players. But he has laughed off suggestions promotion for the Lancashire club means he can now shop in the big bucks sales department.
He said: "We can't spend £8million on players, I assure you."
Ambrose - who joined Celtic in a £1.2m deal from FC Ashdod two years ago - is, however, considered within their budget.
He was handed an improved contract last October, which will run until 2017.
However, after impressing at the World Cup finals with Nigeria, an offer for the 25-year-old is now anticipated.
If Ambrose is permitted to leave, it would make it extremely unlikely that his defensive partner, van Dijk, would also be allowed to move in this window.
With Fraser Forster still being tracked by Southampton - who are reported to be ready to increase their initial bid of £7m to nearer £9m - it would leave a huge hole in the centre of the defence which set a new Scottish shut out record last season.
Deila has made it clear he wants Forster to stay for at least another season.
But, if the Hoops' valuation is met - and cash-rich Saints are not the only club to have registered an interest - his sale would be very hard to resist.
Winning through to the group stage of the Champions League - and the cheque that guarantees - would not only underline Celtic's insistence they do not need to sell, but also provide the big stage platform their top players believe they need.
Forster, Van Dijk and Ambrose will all be key men in the side which hopes to take another major step towards the group stage when they face Legia Warsaw in the second qualifying round first leg in Poland on Wednesday.
Deila will insist that all of his players ignore growing speculation about their futures and focus fully on this crunch game against the Polish champions.
Anthony Stokes is back in the squad after recovering from his slight hamstring strain, and will resume training today.
Deila recognises his side will have to play even better than they did when they demolished KR Reykjavik 4-0 in the second leg of their opening round tie last week if they are to return with a positive result from Warsaw.
The Norwegian is not being suckered in by claims from his countryman, Legia boss Henning Berg, that the Hoops go into the tie as clear favourites.
Deila said: "Every opponent is difficult now.
"Legia are much stronger than KR Reykjavik, and it's a step up.
"They are going to be exciting games and we have a good chance."