Mrs Annan in a recent interview made claims that the ex-Black Stars midfielder has not been doing his responsibility as a husband after he accused her of infidelity and that has affected his attitude towards their children for the past two years.
However, Anthony has denied allegations of not being responsible towards his children.
"It is not true that l don't take care of my kids; everybody who knows my kids will bear me witness. I shop for them any time l am coming from Europe, l check on them frequently via video calls, they are dear to me so under no circumstance will l turn my back on them,” Annan told Accra FM.
"They are my kids so why will l deny them care? I remit them regularly so the allegations by their mother can never be true."
Anthony Annan was part of the Black Stars team that reached the quarterfinals during the 2010 FIFA World Cup in South Africa.
He had a total of 64 caps for Ghana and scored two goals in the process.
The former Hearts of Oak midfielder is currently plying his trade in Israel with Beitar Jerusalem.