The footballer is alleged to have cheated on the singer with 23-year-old model Laura Brown from Newcastle.
He has since visited Burke at her house, where the couple spent five hours deciding whether to continue with their relationship but failed to reach a conclusion.
"They haven't split - they are just deciding what to do," a source told The Sun.
"Alexandra doesn't want more girls coming out of the woodwork and she asked Jermain if there are any more secrets he's hiding.
"They get on so well, she's annoyed he's mucked things up. Jermain has some serious apologising to do."
The pair were first linked in March after being spotted on a date at a London hotel.