According to Edinburgh Live, the Blues have their radar on the former Barnsley man – but face competition from League One rivals Peterborough and Scottish Premiership side Hibernian.
Clark has enjoyed another fine season for John Coleman's side in the third tier.
He's been a key man for 17th-placed Accy, scoring eight goals and creating a further six in 40 appearances.
The 26-year-old is out of contract at the end of this month and is expected to depart Stanley after four years at the club.
His situation has reportedly led to Pompey being interested, although it seems they're not the only potential suitors.
Hibs boss Jack Ross will be well aware of Clark's talents from his time in charge of Sunderland.
He's apparently interested in bringing the former Shrewsbury manager to Easter Road this summer.
Meanwhile, Peterborough boss Darren Ferguson has previously called Clark one of the best players in the league and is linked with a move.
