According to The Sun, the pair, who co-starred in He's Just Not That Into You, spent the evening having dinner in New York earlier this week.
"Jen was giggling like a teenager and giving some pretty intense body language. It's obvious she's really into Bradley," said a source.
Cooper, who stars in the UK box office's current number one The Hangover, denied allegations that he was dating the Friends actress last month, saying he was "very flattered" but that the reports were "not true".
However, the insider added: "Jen is really sweet on Bradley. She says he's perfect physically and she loves his sense of humour. You can expect to see a lot of these two together over the next few weeks."
Aniston recently spoofed on her love life and career at the Women In Film Awards.