Paparazzi photographers claim to have taken pictures of the two driving together in Los Angeles, and a source close to the 'On the Floor' singer confirmed that they spent time together on Saturday.
"After their date in New York, Bradley and Jennifer stayed in touch," the source told People. "She does like his attention, and it makes her feel good that he seems so into her.
"She has fun with with Bradley and he makes her laugh."
Lopez and Cooper were previously linked romantically last month after being seen out to dinner together in New York City.
The singer filed for divorce from her husband Marc Anthony in July after seven years of marriage, while Cooper split from Renée Zellweger in March.
Representatives for both Lopez and Cooper have yet to comment on the alleged relationship.
Watch Jennifer Lopez's 'Papi' music video below: