The two stars grew close while they were shooting 2011 movie The Rum Diary and have been spending a lot of time together since Johnny split from Vanessa Paradis earlier this year.
It's thought Johnny, 49, wants to make their relationship more serious, with recent reports he has splashed out $16 million on a Tennessee estate for himself and Amber, 26. However, she is said to be less keen to make changes to their romance.
"Johnny and Amber have been having a lot of fun spending time with one another, but Amber keeps telling him she’s not interested in being with him in a monogamous relationship," an insider told RadarOnline.
"She says she feels she's too young for him, but the main factor is Amber prefers dating women over men and has no interest in committing to a guy - even if he is Johnny Depp."
Amber has been open about her love for both men and women in the past, although she reportedly doesn't like to put a label on her sexuality.
She may not be looking for anything serious with the Hollywood hunk, but doesn’t want to lose him from her life completely.
"Johnny and Amber get along great as friends with benefits, but where she's concerned, that’s as far as it goes," the source explained.
"Johnny really wants more from Amber, but she’s not prepared to give him that. In addition to him being the wrong sex, she's concentrating on her career at the moment."
The report comes soon after it was claimed Amber had told friends she was serious about her older beau. They were seen enjoying a flirty date in Los Angeles in November, but apparently are yet to make their romance completely official.