The 'All Night Long' singer was seen flirting with the rugby star in the VIP section of London's Chinawhite club on Wednesday night, reports The Sun.
A spokesman for event organisers Londonparties said: "They were laughing and giggling all night and it was obvious where it was going to end.
"They did some grinding on the dance floor before returning to their table - and that's when Alexandra made her move. She pulled Danny off the sofa and gave him a full-on snog."
Another source told Heat World: "Alexandra and Danny were all over each other. They couldn’t get enough of each other, kissing each other’s necks and flirting like love-struck teens."
Although the pair arrived at the club separately, a spokesperson for Burke confirmed to the Daily Mail that they had previously attended dinner together.
Burke and Cipriani allegedly left just after 3am in separate cars headed for the same destination. Burke later tweeted: "Hmm life is sweet! Life is such a flirt!"
Cipriani, who split from long-term girlfriend Kelly Brook last month, has previously been linked with Lindsay Lohan, 90210's Jessica Lowndes and Ashley Cole's former love interest Sarah Purnell.