A representative for Mr Giggs confirmed he is cooperating with police after an alleged incident at his £1.7m Worsley home on Sunday night.
Giggs was arrested and questioned on suspicion of actual bodily harm and assault before being bailed pending further inquiries.
A statement on behalf of the Manchester United legend read: “Mr Giggs denies all allegations of assault made against him. He is cooperating with the police and will continue to assist them with their ongoing investigations.”
Greater Manchester Police earlier released a statement to The Sun newspaper, saying: “Police were called at 10.05pm on Sunday to reports of a disturbance. A woman in her 30s sustained minor injuries but did not require any treatment.
“A 46-year-old man was arrested on suspicion of section 47 assault and section 39 common assault.”
Wales were due to name their squad on Tuesday ahead of November matches against the USA, Ireland and Finland. That announcement has now been cancelled.
A statement from the Welsh FA read: “The FAW is aware of an alleged incident involving the men’s national team manager Ryan Giggs.
“The FAW will be making no further comment at this current time.”
Wales are due to host the USA in a friendly on Thursday, November 12, before facing two home Nations League matches – against the Republic of Ireland and Finland.
Giggs, 46, was appointed Wales manager in January 2018, succeeding Chris Coleman, and has steered them to qualification for Euro 2020, rescheduled for next summer after the coronavirus pandemic forced the tournament’s postponement.
Giggs, who won 64 caps for Wales, had a glittering playing career with Manchester United, winning 13 Premier League titles, two Champions Leagues, four FA Cups and three League Cups.
He is also a co-owner of League Two side Salford City.