The Scotland stand-off has been out of action since picking up a head injury in the PRO12 semi-final with Connacht in May.
Finn is one of seven Glasgow players who will feature for their clubs in the Permiership this weekend.
Peter Murchie, Tjiuee Uanivi and Junior Bulumakau will all play for Glasgow Hawks at home to the unbeaten Watsonians as fourth hosts third in what promises to be a tight clash.
Richie Vernon will try and help Currie record their first win of the season and will face off against his Warriors team mates Nemia Kenatale and Fraser Lyle who will line up for Stirling County.