Insiders say the New York Giants wide receiver began pursuing Rose a few months ago after meeting through a mutual friend. Amber and Beckham have allegedly been texting and talking "like crazy" and have headed out on a few dates.
While sources say the two really like each other, they're said to be taking things slow because the relationship is new.
Aside from Beckham, Amber has been attached to rapper Machine Gun Kelly and Houston Rockets star James Harden since her divorce from Wiz Khalifa.
(Photos from left: Maury Phillips/Getty Images, Al Pereira/Getty Images for New York Jets)