However, the Hoops want the 30-year-old, who has been in fine form this season, to commit to another deal at Celtic Park.
The Hoops boss was reluctant to go into detail about the negotiations but confirmed they are up and running.
"What I will say is that conversations have been had with Artur and his advisors, but whatever we discuss stays in-house," he told the Evening Times.
Scottish Premier Winner 2009/10 Win Outright: Celtic 12/1
Source: Team Talk
Source: Team Talk