Smith Rowe was first called up to the England squad after his strong start to the season with Arsenal.
England have been hit by a string of injuries and Smith Rowe is pushing for involvement against Albania at Wembley on Friday night.
Needing a point from their last two qualifying matches to secure a place at the World Cup in Qatar next summer, England will then face San Marino away on Monday.
Asked if Smith Rowe could make his England debut, Southgate said on Thursday: “We brought him here to be involved with the squad, with a view to being involved in both matches.
“He settled in very well. He obviously knows a few of his club mates, Phil [Foden] since when he was with the Under-17s, and it’s a group that welcomes young players and new players.
“His quality is evident in the way he’s trained so he’s ready. We already enjoyed having him with us this week.