The Mr Selfridge star and former X Factor winner attempted to disguise the fact they were arriving at a party in Mayfair together last Wednesday (January 9), and were later seen checking into a luxury hotel.
"They were both sitting in the back seat [of a shared car]," a source told Heat. "To avoid being seen Jeremy went into the club first, and Alex joined him about ten minutes later, having driven round the block a few times.
Jeremy Piven in Mr Selfridge
"The party had cleared out by 2am and Jeremy and Alex were the last two standing, they were really enjoying each other's company.
"Jeremy left soon after to avoid being seen and went back to the Corinthia hotel. And lo and behold, Alex was seen arriving there just half an hour later."
Alexandra Burke with ex-boyfriend Jermain Defoe
The insider insisted that Burke is "totally [Piven's] type", while the Hollywood star - who at 47 is 23 years older than her - is apparently willing to "really help her career in America".
"He's respected in Hollywood and has amazing connections," they said.
Burke was previously linked to French footballer Dominique Jean-Zephirin, and dated another player, Jermain Defoe, until he reportedly cheated on her twice.