Both clubs enquired about the 28-year-old who has made just two league appearances this season and is out of favour at Tynecastle Park.
Walker’s ability to create and score could strengthen the respective squads in West Lothian or Perth for the second half of the campaign if a deal can be agreed with Hearts.
Tynecastle officials are unlikely to stand in the player's way should he decide to pursue game time elsewhere. He is out of contract at the end of the season and an extension is not on the table as it stands.
A loan move in January would allow Walker to showcase himself in order to earn a deal with a new club for the start of season 2022/23.
He is often left sitting in the stand on matchdays with Hearts unable to give him even the assurance of a frequent substitute’s role since they returned to the Premiership.
He is eager to play regularly in the top flight and remains a favourite among the Tynecastle support. However, his time with his formative club appears to be coming to an end.
Other clubs in Scotland are also monitoring Walker’s situation and could decide to move as the winter transfer window prepares to open on January 1.
Born in Edinburgh, Walker is a graduate of the Riccarton youth academy and made his senior Hearts debut in August 2012. He endured the difficulty of administration and relegation with the club during 2013/14 but helped them regain top-flight status in 2015 after becoming a first-team regular.
He went on to score 15 goals in the 2016/17 campaign and drew admirers from clubs across Britain. Amid talk of a possible Scotland call-up, Hearts rejected several offers from Rangers for their prize asset in 2017.
With his contract six months from expiring, Walker eventually joined Wigan Athletic for a reported £300,000 in January 2018. He stayed only 18 months in England and returned to Tynecastle on a free transfer in summer 2019, signing a three-year deal.