The Easter Road club are working through the complexities of a deal which would see the Australian international return to Leith.
Boyle was sold to Saudi Arabian outfit Al-Faisaly for £3million earlier this year. The club, however, were relegated and Hibs are hoping to navigate their way through a tricky process which involves ‘tax implications’.
He remains a popular player amongst fans and is keen to play at a high level with the World Cup in Qatar coming up later this year.
Johnson has already signed 11 players this summer, revamping the squad he inherited following a difficult campaign which saw both Jack Ross and Shaun Maloney sacked.
The former Sunderland and Bristol City confirmed to Sky Sports his interest in Boyle, revealing he was to “add another forward player".
“We know all about Martin. He’s a good player, and a good lad, and the club loved him in terms of personality but also in terms of his footballing ability," he said.
"I would like to add another forward player to the group but it’s a complex deal and whether or not it’s possible I honestly don’t know.
"If it was possible, of course we’d be very interested.”
Hibs got their league season off to the perfect start with a 1-0 win over St Johnstone at McDiarmid Park on Saturday with a late winner going into the Edinburgh derby at Easter Road on Sunday.
Hearts have sold out their allocation, while the home side are down to their remaining tickets with fewer than 300 left.