The Nigeria defender was one of the Super Eagles to catch they eye during their run to the World Cup knockout stages in Brazil.
But Ambrose is not interested in using the tournament as any kind of launchpad away from Parkhead.
He has two years to run on the contract he signed when he joined Celtic from FC Ashdod in Israel in 2012. And, despite interest from clubs in England, the 25-year-old fully intends to hang around the Hoops for a while to come.
He said: "I have two years left on my contract with Celtic. I am very happy at the club and enjoying my football, and so I will see through my contract."
Ambrose has helped the Hoops collect the league championship in each of the two seasons he has played for the club, and hopes to remain part of the first-choice defence which new manager, Ronny Deila, selects in the coming campaign.
But Ambrose will have to wait to meet up with the Norwegian boss and the squad when they return from their pre-season training camp in Austria.
He is fit and ready to go, despite his 11-month season only coming to an end this week with Nigeria's defeat to France in the round of 16.
But due to his passport situation, it has not been possible for him to get the necessary paperwork to join Deila and the rest of the players in Austria, where they play the first of four friendlies tonight, against Russian side, FK Krasnodar.
The new boss will be delighted to get the action going as he is keen to see which positions he needs to strengthen.
Although Deila does not expect to make many changes to the squad initially, Craig Gordon is expected to be the first to join up with the Hoops.
Deila has also made it clear he wants to add to his options in the wide attacking areas, and the wonder-kid he introduced at previous club, Stromsgodset, could yet be among the players targeted.
Martin Odegaard is still only 15, and has been tipped to be a future star for the likes of Barcelona.
But although he was warned by his successor at Stromsgodset, David Deilsen, that Odegaard is beyond his reach, Deila refuses to dismiss the idea they could yet be reunited in Paradise.
The manager told Norwegian TV2: "It's incorrect to say that Martin is outwith our range.
"Martin must do what is best for him, and we will do what is best for us.
"We'll see if our paths meet at a later date."
Deila did warn, however, that, if Odegaard does find himself a Celt, he would still be a long way from the first team.
He said: "Martin is a good player, but not even close to being a Celtic player at the moment.
"But there's no doubt he might be in the future."
Meanwhile, James Forrest is set to miss Celtic’s Champions League qualifiers due to a thigh strain.
Deila does have some good news to celebrate, however, with Craig Gordon flying out to meet up with the squad after tying up a two-year deal at Parkhead.