Liverpool boss Brendan Rodgers says Raheem Sterling "is being led by his representative" as he seeks a move.
Aston Villa manager Tim Sherwood has revealed in-demand defender Ron Vlaar has told him he wants to stay at the club.
Former Celtic trainee Carey has made 32 appearances this season and his long-range strike against Hearts was this week named the Clydesdale Bank Premier League goal of the season.
Striker Parkin has scored three goals this season following his move from St Johnstone.
Manager Danny Lennon told the Paisley Daily Express: "I've spoken to Graham and he won't be offered a new contract. Sam Parkin will be leaving us too."
Lennon added: "There are one or two who are still under contract but have also been told they can go.
"We are carrying a decent squad but what we have to do in order to allow the young boys to come through is make room for them.
"Football evolves all the time but, with the financial restraints placed on the club, we need people who are going to make massive contributions."
St Mirren could see a major turnaround in personnel with Conor Newton, Paul Dummet and Esmael Goncalves coming to the end of their loan spells.
Goalkeeper Craig Samson is expected to move on, with Motherwell and Kilmarnock vying for his services, while Paul McGowan has stalled on a contract offer amid interest from England.