The film's director, Stephen Frears, has already suggested that he, Mirren and screenwriter Peter Morgan would visit the queen at the palace next month.
"It is speculation, but we are looking at a number of options," a palace spokeswoman said Monday.
Mirren won the Oscar on Sunday night in Los Angeles for playing the monarch in "The Queen," which retells the aftermath of the death of Diana, Princess of Wales, in a car crash 10 years ago.
The Oscar ceremony began at 12:30 a.m. Monday morning in England and was broadcast only on a pay-TV movie channel — making it difficult for most Britons to see it live.
But news of Mirren's win was inescapable Monday, dominating newspaper front pages and television newscasts.
"I'm sure that the queen will be pleased," the palace spokeswoman said.
Mirren, 61, saluted the queen in her acceptance speech for maintaining "her dignity, her sense of duty and her hairstyle" for more than 50 years.
"She's had her feet planted firmly on the ground, her hat on her head, her handbag on her arm and she's weathered many, many storms. ... If it wasn't for her, I most certainly wouldn't be here. Ladies and gentlemen, I give you the queen," Mirren said.