The nine-year-old mare claimed Grade One glory in the Flogas Novice Chase at the Dublin track 12 months ago, but she has failed to strike in four subsequent starts.
She was beaten a length and a half in a mares' Listed event at Doncaster on Sunday and Greatrex is now mulling a return to the top level in open company.
Greatrex said: "I will probably give her an entry in the three-mile Grade One at Leopardstown, but she would only go if the ground dried up sufficiently.
"She won there last year and I sometimes think we are too shy with these mares to keep them to their own sex - she proved it against the boys over there last year."
Although Greatrex felt La Bague Au Roi should have won on her most recent start, he believes it was another step in the right direction.
He added: "I think the mares that finished in the first three at Doncaster were high class. Richard (Johnson) admitted he should have kicked on with her, but when a champion jockey comes in and says sorry, what can you do?
"What he did say was that she felt fantastic and as good as she has for a long time, which was good to hear."
Stablemate Emitom could be stepped up to three miles in the galliardhomes.com Cleeve Hurdle at Cheltenham later this month after failing to beat a rival on his seasonal return in the Relkeel Hurdle at Prestbury Park on New Year's Day.
He said: "Emitom didn't jump a hurdle. He schooled well at home, but that is just him. If you don't jump in races like that, you don't get near them.
"We just gave him some intensive schooling, but it was his first run back from injury and last season I just went steady with him and he took a bit of time to get the hang of it.
"The engine is as good as it gets, but he needs to brush up everything else. A step up in trip might help. The plan was to come back for the Cleeve and it still might be."
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