However, the English Premier League leaders have been told the 34-year-old is not for sale.
The Scotland international has 18 months left on his current contract, having joined Celtic in 2014.
That move followed two years out of the game with knee injury problems, with Sunderland and Hearts the goalkeeper's previous clubs.
Gordon started his career at Tynecastle, having a loan spell at Cowdenbeath before becoming Hearts' first-choice keeper.
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A £9m move to the Black Cats followed in 2007 but injuries took their toll towards the end of his spell on Wearside before he was released at the end of his contract in 2012.
However, after his extended spell away from playing, during which time he did some coaching, Gordon joined Celtic shortly before the club sold Fraser Forster to Southampton for £10m.
Gordon became first-choice under manager Ronny Deila at Celtic Park and helped the club win two Premiership titles and the League Cup in 2015.
When Brendan Rodgers succeeded Deila in May, the Northern Irishman signed Dutch keeper Dorus de Vries and Gordon briefly lost his place in the team.
However, Gordon has started all of Celtic's games since late September, including the League Cup final victory over Aberdeen, and also won his 45th international cap in Scotland's 3-0 loss to England in November.
Chelsea have contacted Celtic with a view to making an offer for goalkeeper Craig Gordon, BBC Scotland has learned.