Southampton won't accept offers for forward Jay Rodriguez or midfielder Morgan Schneiderlin this summer.
Everton forward Kevin Mirallas has hinted that he will sign a new contract at Goodison Park in the summer.
Kilmarnock will hold a media conference on Tuesday where they are expected to announce a new contract for manager Kenny Shiels.
Shiels has been holding protracted talks with chairman Michael Johnston over extending his stay after winning the Scottish Communities League Cup in his first full season as manager.
It is understood details of the contract will be revealed at Tuesday afternoon's Rugby Park event.
After Killie clinched seventh place in the Clydesdale Bank Premier League with a 2-1 win at Dunfermline on May 12, Shiels revealed he had turned down an approach from an English club despite the uncertainty over his future.
The Northern Irishman, who had been linked with the managerial vacancy at Bournemouth, said: "I'm waiting on the chairman getting back to me so hopefully that will be concluded shortly.
"We've got a long-term plan in place and I want something that's commensurate with that.
"I've turned down a job this week. I was offered to go for an interview for a job on Wednesday and I didn't take it because I felt it was unfair. It was an English club, that's all I will say."