Bain joined Celtic on loan from Scottish Premiership rivals Dundee during the January transfer window, and the player has expressed his desire to stay at the Bhoys beyond the summer.
The 26-year-old made a strong impression during the recent Old Firm derby, and Celtic are reportedly in talks to sign him permanently in the summer transfer window.
Hibernian and Heart of Midlothian are also reported to be interested in Bain, which shows the player has plenty of options to chose from in the summer.