The midfielder, who has been hampered by injuries throughout his career, has played more regularly in cup competitions.
However, Southgate questioned how the 34-time international was being used by Arsenal manager Arsene Wenger.
"Jack played as a number 10 all of last season on loan at Bournemouth," Southgate said.
"That is not the way we are playing. When we have played with a 10, we have had Dele [Alli] and [Adam] Lallana, but we are not playing with a 10 tomorrow.
"I don't think Jack is a 10. I think he is a deeper player, but he is not playing deeper. You'd have to ask Arsene why that was.
"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."
Last season marked the first time since 2013-14 that Wilshere made at least 20 league appearances in a campaign as he played 27 games for Bournemouth.