The X Factor winner has been friends with the Tottenham striker for years and apparently started a relationship with him about two weeks ago.
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The pair went on their first public date at the Landmark Hotel in North London last night and were spotted holding hands. Defoe is said to be "buzzing" about the new romance.
"She's a big personality and more than a match for him. A few of the lads have been winding him up at training about it," a source told The Sun.
"They had been in touch for a while, and one thing just led to another. Alexandra had been playing hard to get and a lot of flirting was going on. She finally gave in the other week and they took things further.
"They are both really happy and looking forward to meeting up more often when she comes off her UK tour."
Defoe has previously dated Big Brother stars Imogen Thomas and Chantelle Houghton.
Burke, whose new single 'Elephant' is released on Monday, March 11, recently claimed to be too busy for a relationship.
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