Liverpool legend Gerrard announced his retirement from playing last month and is expected to move into coaching, with a possible return to Anfield seen as his most likely option.
Asked if a potential role with the Three Lions could also be on the cards for Gerrard, Southgate told reporters that he is "looking at" involving former England players with his plans.
"I think what's important is that we have lots of former international players and the doors at St George's Park are always open," he said. "We want to help players that have a desire to have a career in coaching.
"We've had Jamie Carragher in with our junior teams, and obviously Phil and Gary Neville have been involved with our teams in the past, so that is one part of coach development that we're looking at."
Southgate also admitted that he is keen to keep appoint Steve Holland as his assistant and expected to make an announcement on backroom staff "soon".