Jefferies has offered deals to all of them, including Gary Locke, Peter Leven and Allan Johnston.
Simon Ford had already agreed a short-term contract until the end of the year to allow him to overcome a groin injury while Paul Di Giacomo is set to sign a two-year deal.
And former Hearts player Murray - who has played 25 games for Killie since signing from Partick Thistle last summer - will also sign up for a potential two years.
Jefferies said: "I've had talks with all the players and the agents all last week.
"Grant Murray is the only one whose agent has come back to me, he has accepted a contract of one year with a year's option.
"The other agents will follow. I've got one who deals with three or four players, so by the time he gets round everyone, he will come back to me at the start of the week.
"All the talks have been done and the offers have been made. It's now in their hands."
Jefferies may be on the hunt for a new goalkeeper after Graeme Smith rejected a new deal, while third-choice keeper Chad Harpur is also out of contract.
The Killie boss explained: "Graeme Smith unfortunately for us has turned the offer down, and he maybe looks to try and get a better offer elsewhere.
"That's his prerogative and we hope he gets it and does well but we have to work within our budgets."
Killie forward Paul Di Giacomo has also signed a new 2 year deal with Killie after performing well in recent games,
everyone at killiemad hopes that Paul will grab this chance with both hands and fulfil his early potential, starting with the against Celtic on sunday at Rugby Park