The former Scotland Under-21 international joined the Bhoys from Scottish Championship outfit Hibernian in the summer transfer window, but he has struggled for playing time so far this season.
“When he first arrived, I felt there were a lot of players at the club who were very similar to him and therefore it might be difficult for Allan to get games,” former Celtic midfielder and manager Hay has written in The Glasgow Evening Times.
“But the injury to Scott Brown and loss of form to one or two others means that Allan, for me, is due a run.
“He came on at Inverness and his great pass led to Kiernan Tierney setting up a really well-worked goal. It will be interesting to see how he does."
Celtic are on course to winning the Scottish Premiership title this season. The Hoops are at the top of the league table at the moment with 39 points from 16 matches.
Ronny Deila’s side are as many as seven points clear of second-place Aberdeen, and the title is now theirs to lose.
Celtic, who defeated Inverness Caledonian Thistle 3-1 away from home last weekend, will take on Hamilton Academical at Celtic Park in the Scottish Premiership on Saturday afternoon.
Hamilton are fifth in the league standings at the moment with 22 points from 16 matches.