Reports in Scotland claim there is some confusion over what happens now with the ex-Dundee United and West Brom midfielder.
The Dundee Evening Telegraph claims that the two clubs are in talks over a potential return to Parkhead for the 25-year-old because of his ongoing struggles.
The Dens Park club are said to be in the dark over the plans for the player’s recovery.
Allan will be out of action until November but Dundee boss Neil McCann admitted they were waiting on guidance from Celtic over what happens next.
“Because he’s a loan player we, quite rightly, have to be guided by Celtic and their medical staff,” McCann said, as quoted by the Evening Telegraph website.
“It’s early days and we’re just waiting.”