Chelsea have had a £3m bid rejected by Celtic for the Scotland international keeper, who they see as Asmir Begovic's potential replacement.
Bournemouth have made an offer worth £10m for Begovic, but Chelsea won't let him leave unless they can find someone else first.
The Blues have already been turned down by Spain international Diego Lopez, who is currently on loan from AC Milan at Espanyol.
But Gordon is believed to be tempted at the possibility of making the switch to Stamford Bridge, even though he will only be back-up to first choice Thibaut Courtois.
The 34-year-old has plenty of experience of the Premier League having played for Sunderland between 2007-12.
However, Celtic have already made it clear that they want Gordon to stay, with boss Brendan Rodgers saying: "Would Chelsea be wasting their time? Yes, of course. If it is the case they are interested, we don’t want to sell."
London Football! Stay on top of all the news and gossip from the January window in our transfer section.
