The 30-year-old goalkeeper has been training with his loan club in East Lothian.
Bogdan will provide competition, and well as back-up for the injured Ofir Marciano.
Bogdan joined Liverpool from Bolton Wanderers in 2015 after making 120 appearances across all competitions.
He was named Player of the Year in 2012, before moving to Anfield on a free transfer in June 2015.
The Hungarian international player was rarely called into action at Liverpool, and appeared just six times before he went on loan to Wigan Athletic.
In November 2016 he suffered an ACL tear and hasn't played since.