The game would be Sterling’s 50th cap for his country, coming when he is only 24 years old.
Later on Saturday it was revealed Southgate considers him a potential captain, should regular skipper Harry Kane have to miss out on the Nations League Finals with injury.
“Raheem is in that leadership group now and he has fulfilled that brilliantly over the last 12 months in particular,” Southgate told a press conference.
“You can see his maturity now with what has happened to him on and off the pitch. I think he is realising that.
“He has risen to that challenge and embraced it and I wouldn’t have any hesitation in making him captain if that was the right thing.”
The winger was criticised for a goalless World Cup, but since October has scored six goals while on Three Lions duty, including a hat-trick against the Czech Republic in March of this year.
Sterling was named PFA Young Player of the Year, and the Football Writer’s Association Player of the Year, in addition to picking up the FA Cup, Carabao Cup and a second consecutive Premier League trophy.
He has scored 26 goals in all competitions for Manchester City this year, his best return in a single-season.
Kane has been named in the Nations League squad but has not appeared in a game since limping off in a game with Sterling’s City in the Champions League on April 9.
Kane faces a dash to be fit for Spurs’ Champions League final on June 1, as well as England’s Nations League campaign.