The Leicester City defender, who turned 30 on Wednesday, and former partner Stephanie Ward, 29, had a public row on Twitter, in which Simpson accused his ex of denying him the chance to speak to their daughter on his birthday.
Miss Ward responded angrily to the claims, saying that he had chosen not to spend the day with their five-year-old daughter Skye.
She also said that she had been offered a restraining order after Simpson was convicted of assaulting her in May 2015 at his home in Worsley, Manchester, but refused as she 'didn't want it to affect Skye'.
Miss Ward has reportedly demanded that Simpson pays more child maintenance each month.
Despite the public row, she has allegedly said that she will drop these demands if he gives her another baby as she wanted her children to have the same father.
A friend of Simpson told : 'Stephanie has told Danny that she wants considerably more a month.
'But she promised if he gave her another baby she wouldn’t ever ask for an additional penny from him again.
'She has even told him she’d happily have artificial insemination if he doesn’t want to sleep with her again after their difficult split. It comes after the angry spat on Wednesday, in which Miss Ward said that 'no man should be able to bully or lie about a woman'.
The row began when Simpson tweeted on his 30th birthday: 'When you FUND your exes (sic) whole life and can't even get a happy birthday message off your child. What a world we live in lol #happybirthday.'
He continued: 'Turning 30 makes you think it's time to start opening your mouth and stop keeping quiet because you kick a footballer.'
--dailymail