Several teams in the English Football League Championship and League One are keen to sign the Scotland goalkeeper, who turns 39 on Friday.
He is hopeful of staying at Hearts after rejoining his formative club in summer 2020, but a new deal has yet to be signed. His current agreement expires at the end of this season.
Clubs south of the Border are monitoring the situation closely in the hope that they may be able to prise Gordon away and take him back to England. He spent five years there as a Sunderland player between 2007 and 2012.
Talks between Gordon and the Hearts hierarchy are ongoing in an attempt to ensure the club skipper finishes his career with the team he has supported since childhood.
He was appointed captain in summer this year after Steven Naismith retired from playing and has performed superbly all season in the Premiership.
Hearts sit third in the league table and hold a five-point advantage over fourth-placed Motherwell, with the top flight now on a rearranged winter break for three weeks.
Gordon's goalkeeping has been a huge factor in the results so far this term and Tynecastle officials are confident they can keep hold of the influential veteran.
He is one of a number of first-team players whose contracts are set to expire within the next six months. Michael Smith, Peter Haring, John Souttar, Craig Halkett, Stephen Kingsley, Andy Halliday, Armand Gnanduillet and Jamie Walker are also in the same position.