Celtic manager Brendan Rodgers expects captain Scott Brown, Leigh Griffiths and James Forrest all to sign new contracts at the club.
Midfielder Brown, 33 signed from Hibernian in 2007, while striker Griffiths, 28, joined from Wolves in 2014.
Winger Forrest, 27, came through the Hoops' youth academy and made his first-team debut in 2010.
Ahead of tonight's trip to St Mirren in the Scottish Premiership, Rodgers said: "We are pretty close on Leigh. He clearly wants to be here, we want him to be here, so that will be good news. We think that is not too far away.
"Scott has made it clear he wants to be here and I am sure there will be a deal done pretty soon on that. He is quite relaxed about it. He knows what we think of him here at the club so hopefully that will be done.
"James and his people will be speaking with the club and, likewise, a player we would love to extend here because he has been absolutely brilliant in my time here."
Meanwhile, Celtic keeper Craig Gordon called for clarity in the Scottish Football Association's "clouded" disciplinary procedure which he suggests leaves them open to questions around club allegiances.
A rule book change during the summer has resulted in several controversial decisions this season, the most recent being when a panel of three former referees decided that there was no case for Rangers keeper Allan McGregor to answer after his kick out at Hoops defender Kristoffer Ajer during the Old Firm game at Parkhead. Gordon said: "It seems quite a clouded subject in how they get to the decisions.
"As far as I am aware it goes to the three (former) referees, that there is no comeback, you don't know who they are. It is a strange system.
"You never know who the referees are, who their allegiances (to) might be.
"I just think that is probably not the best way to go about it."