Us Weekly magazine reported that Bynes on Wednesday tweeted a photo of Cyrus along with the words "Ur ugly."
The tweet did not appear in Bynes' feed on Wednesday night, but the 27-year-old former child star also defiantly tweeted on Wednesday: "This is my twitter. I say whatever I want. Thanks!"
The troubled "Easy A" actress has been the focus of tremendous scrutiny in recent months for her bizarre public behavior, recent legal troubles involving the New York City Police Department and her negative Twitter remarks about numerous celebrities, including Rihanna, Lance Bass and Jay-Z.
In a Wednesday interview with Hot 99.5, a Washington, D.C., radio station, Cyrus, 20, was asked about Bynes.
At first, she said she didn't want to address the issue, but then added: "I think it's all so sad that I don't want to add any fuel to that fire, because it's really so sad to me. And you know, [I] was rooting for her to come back until she started attacking me."
The singer added: "I just thought it was hilarious that she mentioned my name the moment I was the worldwide trending topic on Twitter. It's just funny 'cause the moment you're, you know, a trending topic, it's funny how many people want your name to come out of their mouth so, somehow, they can associate and maybe they can be a trending topic."
"There's speculation that Amanda and Liam [Hemsworth], Miley's fiancé had a little fling in 2009 and some people think this may be the reason that Amanda is lashing out at Miley," said Howard Bragman, a longtime publicist and ABC News consultant.
Bynes' increasingly erratic behavior has raised questions about her mental health, and she was arrested on a drug charge on May 23 when police accused Bynes of throwing a bong out the window of her Manhattan high-rise apartment.
She has denied the allegations.