The 25-year-old spent last season on loan at Bournemouth before sustaining a season-ending injury in April but has returned to the Arsenal starting line-up during their Europa League fixtures this campaign.
"Jack played as a number 10 all of last season... ," Southgate told reporters. "That is not the way we are playing. When we have played with a 10, we have had Dele (Alli) and (Adam) Lallana.
"I don't think Jack is a 10. I think he is a deeper player, but he is not playing deeper.
"But I want to be clear: I really like Jack Wilshere as a player. I think he is a talent and I really respect him as an individual. And I'm hoping that we are in a position in March where we can pick him."
Wilshere, whose contract expires at the end of the season, has scored twice in eight appearances for Arsenal but is yet to start in the Premier League.
The playmaker expressed his love for the London club, saying he would like to extend his 10-year stay at the Emirates and fight for his spot in the starting XI.
"I've been here 10 years, I love this club and feel like I have a special relationship with the fans," Wilshere told Standard Sport. "Of course I want to stay.
"At the moment I'm concentrating on getting into the Premier League team. I've been playing quite a lot of football and I'm happy with where I am fitness wise but I want to be playing for Arsenal in the league."
England play Brazil on Tuesday before the league resumes with Arsenal hosting Tottenham Hotspur in the north London derby on Nov. 18.
(Reporting by Aditi Prakash in Bengaluru; editing by Amlan Chakraborty)
