Kilmarnock have offered three-year contracts to captain Manuel Pascali and fellow defender Alex Pursehouse.
But chairman Michael Johnston also said that players would be leaving in January, with some new faces arriving at the Ayrshire club.
"We have entered into negotiations with the pair, offering them three-year contracts on improved terms," he told BBC Scotland.
Indeed, Johnston is hoping Pascali will end his career at Rugby Park.
"Manuel has been here for three years now and he is a player we want to keep until the end of his career," said Johnson of the 30-year-old Italian who arrived at the club after leaving Parma in 2008.
"Garry Hay and James Fowler have both been given testimonial years.
"These are players who have shown commitment to the club and we would like to do the same with Manuel.
"He is going to give our offer careful consideration.
"We hope to hear from him soon and obviously we are hoping it will be favourable news."
English 19-year-old Pursehouse signed for Kilmarnock this year following his departure from Tranmere Rovers.
"Alex played for our under-19 team and progressed to the first-team, where he has made a number of starts," added Johnston.
"We want to develop him as a player, but we need that security of knowing that he is here for the long term."