Twilight actress Greene, who split from Joe Jonas in March 2011, was rumoured to be engaged in a feud with Lovato, who ended her relationship with the Jonas Brothers singer in May 2010.
However, Greene has since insisted that she has no ill will towards Lovato and expressed frustration over the stigma in Hollywood that women who have dated the same man cannot get along.
"I'm really happy that she's doing well. She and I never had a problem with each other, but, you know, it doesn't go away. Jen Aniston still gets asked about Angelina Jolie," Greene explained in an interview with the forthcoming November issue of Allure.
Asked to describe her ideal partner, Greene explained that she likes many different types of men, saying: "I go through stages. Randomly, I'll be attracted to a crazy rocker with tattoos. And I find that I'm extremely attracted to ambition and wit."
Jonas recently denied that he and Greene had reunited following reports which claimed that they had recently hooked up while in Las Vegas.