Pressley played his last game for Hearts in November

Pressley, 33, left Hearts on Saturday, having spoken of dressing-room unrest under the regime of club owner Vladimir Romanov in October.

The Ibrox club, Dundee United, Leeds and Derby County are thought to be competing for the defender's signature.

Pressley has been at Tynecastle since 1998 but recently fell out of favour.

He was omitted from the squad for November's game at Falkirk amid reports of a plot to remove him as captain.

Pressley is ineligible to play for any new employer before the opening of the transfer window in January.

His last game for Hearts was in November's 0-0 draw at Inverness Caledonian Thistle last month.

"I have enjoyed my time at Tynecastle enormously and will be sad to leave," Pressley told the Hearts website on Saturday.

"Particularly, I would like to thank the fans for their support during my time at the club."

Pressley lifted the Scottish Cup in May following a successful season and many point to his presence in the dressing room as the main reason for that run of good form.

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Hearts head coach Valdas Ivanauskas had been silent on the issue but had recently claimed that Pressley was the club's "cement".

"It has been a difficult few weeks for both the club and Steven," said Ivanauskas.

"We recognise the tremendous contribution that Steven has made - both as a player and as captain at Tynecastle over the years - and we wish him all the best for the future."