According to reports, Paul stabbed two men during an altercation in Formby last month.
A police spokesperson said: “Merseyside Police can confirm a 56-year-old man has been charged with two counts of Section 18 wounding and one count of Section 47 assault following an incident in Formby on Friday [25 September].”
Former Sugababes singer Heidi, 32, previously revealed that she and her dad lost contact after his divorce from her mum.
But earlier this year she said: “A couple of years ago my dad had a brain tumour, but luckily we’d made contact just before that.”
The news of her dad’s arrest come after she announced her engagement to Alex Partakis.
Taking to Twitter to share the news, Heidi wrote: “Delighted to share the news that my gorgeous @alexpartakis proposed last night!
“Am the happiest girl alive and can’t wait to be Mrs HP [sic].”
Heidi has yet to comment on the reports of her dad’s arrest.