Celtic manager Ronny Deila and chief executive Peter Lawwell have held talks about keeping Craig Gordon, following speculation that Chelsea are interested in signing the goalkeeper in the summer.
Petr Cech looks likely to leave Stamford Bridge at the end of the season, and Jose Mourinho has reportedly identified Gordon as a potential replacement.
"I think he's a great goalkeeper and he's a man we want to keep at the club," Deila told The Herald.
"We will do everything to keep him here. I understand why other clubs are looking at him because he's had a fantastic season. Myself and Peter have already talked about this. It's also about what Craig wants and hopefully he wants to stay here and be with Celtic. I want him here for the rest of his career. Hopefully that can happen.
"It would be a shame but I don't think he wants to do that. He wants to play football until the end of his career and we want him to stay here."
The 32-year-old has conceded just 25 goals in 37 matches this season.
