Rangers want to sign Lawrence Shankland before this summer's World Cup, it is understood.
The Hearts Standard reports that the Ibrox side are pushing to bring the striker, who scored 20 goals in 34 appearances for his club this season, to Glasgow as part of their summer rebuild.
Shankland signed a new three-year deal with Hearts last summer, but his future is now up in the air.
He will soon travel to the United States to compete in the World Cup with Scotland. Rangers are keen to push through a deal prior to the tournament.
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Hearts are already said to be in the process of identifying potential replacements for their captain, who joined from Beerschot VA in Belgium four years ago.
A deal is already in place for the Tynecastle side to sign Josh McPake this summer, and French midfielder Tom Renaud is set to follow.
Hearts are also progressing with moves for defenders MJ Kamson-Kamara and Malachi Fagan-Walcott, as well as Falkirk's Calvin Miller.