The FA, who are believed to be interviewing only Southgate for the permanent manager's role, will confirm their decision shortly and are keen to have former players in alongside the head coach, according to the Daily Mail.
Gerrard has been linked with a host of playing and non-playing roles ranging from Inter Milan to MK Dons, and of course Liverpool. Lampard has been touted for a return to Chelsea, where he made over 420 appearances.
Any final decision on coaching appointments will be left until the five-man panel have confirmed the team's new manager, but Ashworth is believed to rate both former England stars as future coaches, capable of aiding the Three Lions.
Gerrard, who worked with LA Galaxy U18s in the states, is currently undertaking his UEFA licenses and has previously expressed his desire to work with the national set up once his playing career comes to an end.
The speculation over backroom staff comes in the wake of revelations and subsequent fall out over certain players' antics during the international break.
Sky Pundit Gary Neville previously performed a player liaison role under Roy Hodgson and it could be that Ashworth is interested in bringing in former senior players to help curtail disciplinary incidents.