"The Words" co-stars had intended to spend the holidays with Cooper's family in Paris, but ended their romance shortly before Christmas. Saldana ended up celebrating with her own relatives in Miami, the newspaper said.
No specific reason was given for the breakup.
UsMagazine.com said Cooper and Saldana initially split up in March 2012 following a three-month courtship, but reconciled in the fall.
Cooper is best known for his work in "The Hangover" comedies and the current awards-nominee "Silver Linings Playbook."
Saldana has appeared in the films "Avatar" and "Star Trek."