
Eckert’s future remains uncertain after his FA disciplinary hearing over his role in the Spygate scandal took place on Thursday.
Saints are now waiting to discover the verdict, with contingency plans being considered in case the German is handed a lengthy suspension.
The Telegraph claim Edwards has been discussed as a potential interim appointment should Eckert receive a ban which prevents him from working.
READ: Eckert in FA misconduct hearing over Spygate scandal
The 43 year old was sacked by Wolves in June following their relegation from the Premier League and replaced by Portuguese coach César Peixoto.
Edwards has previously managed in the Championship with Luton and Middlesbrough, while Saints are reported to have been long-term admirers.
Eckert was charged with misconduct by the FA in July after Saints admitted spying on three Championship opponents last season.
The club were subsequently expelled from the Championship play-offs and handed a four-point deduction for the current campaign by the EFL.