The former Hibs star has failed to make an impact at Parkhead.
Celtic's Scott Allan on the pitch before the match
The 24-year old joined the Hoops from Hibernian last year after impressing in the Championship but failed to force his way into the first-team under previous boss Ronny Deila – making just 13 appearances in all competitions.
Celtic manager Brendan Rodgers
He has similarly failed to impress new manager Brendan Rodgers over the summer and he is deemed surplus to requirements ahead of the new campaign.
Celtic are well-stacked in the midfield department and Allan would have found first-team football hard to come by had he stayed at Parkhead this season.
Celtic's Scott Allan (R) in action with St Johnstone's Chris Millar
A move to Championship side Rotherham will allow the promising Scot more playing time and the chance to show he can come back to Glasgow next season ready to make an impact.
Alternatively, his stint away could up his market value ahead of a permanent move to a club down South should he impress sufficiently enough.
Celtic face FK Astana tomorrow in the second leg of their Champions League Third qualifying round tie and will be determined to progress to the Play-off stage.