Sam Nicholson has rejected a new contract offer from Hearts, alerting clubs in Scotland and England to his availability.
The 21-year-old is currently recovering from a knee injury and is out of contract in six months' time. Tynecastle officials made him a formal offer of an extension, which has been refused. They remain hopeful that he could be persuaded to stay.
Rangers are one of many clubs monitoring the situation ahead of the January transfer window. The winger will be entitled to talk to any interested club about a pre-contract agreement in the New Year, although he is not expected to play again until late January after undergoing knee surgery.
Nicholson is focused on regaining full fitness and will then make a final decision on his future. Under FIFA rules, Hearts would be entitled to between £400,000 and £450,000 compensation if he leaves on freedom of contract at the end of the season.
He joined the club aged 12, is a graduate of the Riccarton youth academy and made his first-team debut in August 2013.