The English Premier League side wish for the 34-year-old to play back-up to No.1 Thibaut Courtois, as current deputy Asmir Begović is expected to join Bournemouth on loan.
Chelsea have wasted no time since their interest in the stopper became public yesterday, but the Parkhead side have been swift in rebuking their advances.
Last night manager Brendan Rodgers insisted Chelsea will be wasting their time with any move for the Scottish international.
Rodgers is determined to hold on to Gordon who kept another clean sheet last night as the Scottish champions defeated St Johnstone 1-0 to stretch their lead at the top of the Premiership to 22 points.
“If it’s the case, then yes [they are wasting their time],” said Rodgers. “We don’t want to sell him. His contract is up at the end of the season but with an option for the club.
“It’s not something we will even consider, really. He’s someone I want around for the duration of my time here. He’s a good guy, he is very happy in his life at the moment and really enjoying his football. It has given him an edge to his game. If a club like Chelsea is interested in him, then it shows the level they see him at.
“I heard something before the game and I’m not surprised. It’s another indication of where this team is at that Craig is speculated about.
“It’s a big testament to him. There is a lot of speculation around a lot of our players. They are playing at such a level that these great clubs are interested in them. But Craig is very much a part of what I’m doing here. He has really consolidated his game, how we want to play. You see how composed and calm he is. He is 34 and can go on for a number of years yet and be a real pillar of this team.”