The former Manchester United winger is 'ready' to return to return to the dugout if results do not improve at the League Two side, reports The Sun.
The Welshman stood down as Wales manager in June 2022 after being accused of controlling and coercive behaviour against his ex-girlfriend Kate Greville between August 2017 and November 2020.
In August 2022, following a four-week trial, jurors failed to reach a verdict on the case in question after more than 20 hours of deliberations.
Domestic abuse charges against Giggs were withdrawn in July, meaning that a retrial was abandoned. Giggs plead not guilty to the charges, which also included assaulting Kate's sister Emma, and judge Hilary Manley ruled he was found not guilty on all counts.
Now, The Sun claims the 49-year-old could replace manager Neil Wood at Salford; where he is a co-owner alongside Class of '92 team-mates Gary Neville, Phil Neville, Paul Scholes, Nicky Butt, David Beckham - plus Singaporean businessman Peter Lim.
The Ammies sit 19th in League Two, having lost four games in a row, but have targets to reach the play-offs for the second season running, after finishing seventh last term.
Giggs had a 48 percent win record as Wales boss between January 2018 and November 2020 during his 25 games as manager. Stand-in Wales head coach Rob Page succeeded him and has remained in charge ever since.