Southgate has admitted that the two England legends could have taken easier roles, and acknowledged that he was happy to assist either man during the early stages of their respective jobs.
At a press conference, Southgate told reporters: "They both know if they ever want to speak about anything, I'm more than happy [to talk].
"They're two very good characters. In particular, I think, it's great to see two lads that have a lot to offer the game, stay in the game.
"There's an easier route to go - they haven't taken that and that's brave. Both of them, I'm sure, could have a far more comfortable life, but maybe not as fulfilling. They're going to have a different type of challenge. They're going to be developing different skills, having different experiences.
"It's great that they have the opportunity to put back into our game. We want more England coaches. In the future, when the England manager's job is available, we want lots of high-quality candidates."
Between them, Gerrard and Lampard represented the Three Lions on 220 occasions.