Midfielder Ian Black and goalkeeper Michael Fraser have rejected contract offers from Caley Thistle.
Inverness director of football Graeme Bennett still believes the pair will stay at the Highland club and the agents of Black, 23, and Fraser, 25, are still in discussion with Caley Jags after turning down improved terms at the Caledonian Stadium.
The players are out of contract at the end of this season and free to negotiate pre-contract agreements with other clubs next month.
Don Cowie, who is also a free agent in the summer, will start new contract talks only when the January transfer window opens.
Bennett said: “We would have preferred to tie these players up earlier in the season but they have been open with us.
“We appreciate their situation. They are young men and have to try to assess what is best for themselves.
“We made Michael Fraser an offer and his agent turned it down, but dialogue will continue between us. We are keen to keep him.
“Michael is a good goalkeeper and we need two good goalkeepers at the club – we think we have that at the moment.
“Ryan Esson came to us, bided his time and Michael has to keep working away at his game and I am sure his chance will come again.
“It is up to them to battle it out and we want competition for every place at the club.”
While it would be no major surprise if Fraser was to stay at the club, the same cannot be said regarding Black and Cowie.
Bennett said: “We made Ian Black an offer and his agent knocked it back but we will keep talking to him.
“Hopefully, a compromise will be reached.
“Don Cowie has made it quite clear his agent will speak to us shortly and he has said that since the beginning of the season.
“I would love to give every player what he wants but we have to try to work within our budget.
“We will continue to try to keep Cowie and Black at the club. They are key parts of the team.
“We want these players to stay and be the stalwarts of the club for the next six or seven years – just as Ross Tokely and Richard Hastings have been.
“We have built a club on stability and we see these players as being the next generation.
“We are still confident they will stay with us.”