Sunderland boss Roy Keane has rekindled his interest in the Scotland goalkeeper after having a £5m bid rejected by the Edinburgh club last month.
Aston Villa also want to take the 24-year-old to the Premier League.
A £9m transfer to either of the English clubs may be concluded before Monday's Edinburgh derby at Tynecastle.
The Edinburgh club's majority shareholder Vladimir Romanov has indicated he would be willing to sell Gordon if the player said he wanted to leave.
BBC Sport understands Gordon is holding talks with Keane, and Aston Villa boss Martin O'Neill.
Speaking last week , Gordon was reluctant to comment on the transfer speculation.
"The club hasn't told me what kind of figure they want for me, but that's up to them," said Gordon.
"I'm the captain of this club and with that comes responsibilities. I can't take my eye off the ball. I need to concentrate fully on the job."
Stevie Banks, who has been Gordon's understudy for the past two seasons, is expected to play against Hibs.
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That will break the record for the price paid for a British goalkeeper. Whenever I watch Scotland in Internationals he has always impressed me, so taking the step up from the Scottish League to the Premiership shouldn't be a problem for him. He was one of the goalkeepers along with Artur Boruc and Shay Given that I wanted to replace Jens Lehmann at the end of last season.
The Martin O'Neill factor will probably make him choose Villa.