Scott McDonald is in talks to sign a new contract at Celtic, while Shunsuke Nakamura expects to be at Parkhead next season.
Australian striker McDonald has had a major impact in his first season with Celtic, scoring 31 goals since his move from Motherwell last summer.
He is now set to be rewarded for helping the club retain the SPL title by agreeing a new deal during the summer.
"My agent, Lou Sticca, flew from Australia for talks with Peter Lawwell last week," said McDonald.
"He told me that things had gone well, but I said I didn't want to know any of the details.
"I wanted to concentrate on our match against Dundee United and winning the title. Everything else could wait.
"Now that we've won it, it's the most incredible feeling I've experienced, and I want more of this.
"That's why I'm so thrilled at the prospect of signing a new deal and making sure I've got a few more years of winning trophies for Celtic in front of me."
Meanwhile, Japanese midfielder Nakamura is looking forward to a longer summer break before extending his Celtic career into a fourth season.
Nakamura said: "It is a big thing for me that we have gone straight into the Champions League.
"Because we don't have to qualify, I can get maybe two more weeks off.
"I didn't get a proper break last year when we had a qualifier and had to report back to the club earlier than usual. So I think I will be at Celtic for one more season."