The Hangover star was spotted out at dinner with Lopez over the weekend.
"It was a date," a source told Us Weekly.
The insider continued: "[Cooper] has been after her for ages - calling her for a while."
Lopez filed for divorce from husband Marc Anthony in July after seven years of marriage.
A spokesperson for Cooper denied the date reports, saying that the dinner was "for business regarding a project".
Earlier this month, Anthony dismissed claims that he and the 'On The Floor' singer split due to an extra-marital affair, insisting that he had not engaged in a romance with HawthoRNe co-star Jada Pinkett Smith.
Cooper split from previous girlfriend Renée Zellweger in March. The two started dating in August 2009.