The talented mare knocked a joint when schooling in preparation for the Hatton’s Grace Hurdle at Fairyhouse in November.
It had been thought she would have to head straight to the Cheltenham Festival without a run, but Mullins has not completely ruled out the chance of giving her an outing beforehand.
“I’m much happier with Annie Power,” he said.
“She’s riding out and she’s recovering as quick as I’d hoped. I’m able to bring her forwards a little and hopefully she’ll maintain that and she doesn’t go backwards.
“I’m keeping her comeback as Cheltenham but if we can get a run before that would be a bonus.
“At the moment, she’s just going for the mares’ race but now she’s a little more forward and if we get a run into her we’ll see.”
Meanwhile Coneygree remains in Newmarket for further treatment on an injury that seems likely to rule him out for the season.
Mark Bradstock’s Cheltenham Gold Cup hero, who looked so impressive on his return to action at Sandown in November, had been in the frame to run over Christmas in either the King George VI Chase at Kempton or in the Lexus Chase at Leopardstown, but is now sidelined after suffering a hock problem.
While the injury is not thought to be career-threatening, Coneygree is not expected to return to action before the end of the current campaign and has been removed from ante-post lists for the Gold Cup.
Sara Bradstock, the Oxfordshire trainer’s wife and assistant, said: “He’s in Newmarket (Equine Hospital) and is still being assessed by Ian Wright, who is one of the orthopaedic surgeons there.
“All he has told me so far is that he’s injured his hock, they are dealing with it and that the long-term prognosis is good.
“He’ll be back for sure, whether that is for the end of this season or next season, we don’t know at this stage.”
Bradstock insisted Coneygree will not be rushed back into action if he is unable to defend his Gold Cup crown in March.
She said: “He’s had time off before and we’ve brought him back, so we know we’re able to do that – we know the horse has the enthusiasm to come back from a lay-off.
“He can still win another Gold Cup, whether that’s this season or next.
“With a lesser horse, you might try and squeeze in something at the back-end of the season, but if he isn’t going to make it (Gold Cup), we might as well give him the time (to recover) – that’s the way I’m thinking about things at the moment.
“As soon as we know how long he’ll be out for, we’ll let people know, but I don’t know when that will be at the moment.
“He’ll stay in Newmarket for a few days, anyway.We’ll see what happens”