The 21-year-old has impressed in the number 10 shirt recently but is out of contract next summer.
According to Irish sports website,The42, Healy is Scottish-qualified and an offer from Glasgow with the possibility of international rugby with Scotland would involve a big financial leap from his current academy contract.
With the IRFU's pause on any contract negotiations due to Covid-19 set to extend into January, the future of a number of Irish players - including Healy - is uncertain.