Representatives for both stars denied that they were an item last month, but the pair have recently been snapped kissing in public.
Saldana and Cooper are now seriously dating and even made plans to spend time together over the holidays, an insider told E! News.
A source close to the couple added: "They are totally dating."
Cooper and Saldana's reps have not commented on the latest report.
Saldana called off her engagement to fiancé Keith Britton in November after an 11-year relationship.
Cooper was previously married to actress Jennifer Esposito and also dated Renee Zellweger for several months.
In November, Cooper was named the 'Sexiest Man Alive' by People magazine.
> Bradley Cooper interview: 'Todd Phillips is working on Hangover 3'
> Ryan Gosling makes Bradley Cooper question 'Sexiest Man Alive' title
Watch Bradley Cooper in the trailer for Limitless below: