The team resumed training yesterday and head to Suva on a charter plane tomorrow.
Squire injured his shoulder in the second test against France and did not play the third test at Forsyth Barr Stadium last Saturday.
It was hoped he would be right for the match in Fiji but Highlanders assistant coach Glenn Delaney said the loose forward was unlikely to make it this Saturday.
Delaney said all the other All Blacks who had come back into the camp were in good nick and fitted in straight away.
''They have been in camps all year so again it has become pretty normal for us to get them back. What our All Blacks are great at doing is getting out of one environment and coming back to another,'' he said.
Seven Highlanders made the field for the All Blacks on Saturday, which was pleasing for Delaney.
''They did themselves proud and made us proud and we're pleased to see them back. It is always exciting to see guys realise their potential. Some guys are only just starting their journey. Others are well through it, and getting better.
''One thing we like is our guys always like coming back and seeing the boys here. Our environment is very different from the All Black environment. That is based on our culture, context and people. The guys love coming back to us. They love the All Blacks but once they come back here they are 100% Highlanders.''
The Highlanders trained indoors at the Edgar Centre yesterday, getting away from the Dunedin chill.
Delaney is looking forward to the warmer climes of Fiji.
''Last time I went to Fiji it was my honeymoon. It is an opportunity to take the Highlanders on the road and see some new people. We have some strong connections there with Waisake [Naholo] and Tevita [Nabura] and a lot of old Landers over there.So we will be linking up with them.Just a great opportunity to meet some new fans over there.''
The team had a hit-out last week in Invercargill with a solid 29-10 win over the French Barbarians.
''Some of the guys made their debuts. Everyone has played for us this year which is important to us.
''Both sides of the ball we could try things about the game without the pressure of competition points. Not withstanding that, we were there to pay respect to a national side and it was good to come away with a result.
As a forwards coach he was really pleased with the performance
''The foundations, you've got to keep building. Look every time you get an experience like that it can build confidence and that is what we want.
''We want to have a team that is confident to play our way. We know we have a big challenge against the Chiefs this week ... they're a well coached team who play a mean game of footy and a tough team to break down.''