The Rugby Football Union's Club England committee meet on Thursday, with elite rugby director Rob Andrew set to present his thoughts on the way forward following Robinson's exit.
Harlequins director of rugby Richards is a strong contender for the job after his success at domestic and European level with Leicester, but insists it is far from a fait accompli.
"If someone knocks on my door, I would listen," Richards told the Daily Mail.
"But, and it is a massive but, a lot of questions would have to be asked. Things would have to be right. I haven't been approached."
The Club England committee must decide whether to appoint someone in the short term to see them through next year's RBS 6 Nations Championship and the defence of the World Cup or to find a long-term successor to Robinson.