The 25-year-old, back in North London following a season's loan at Bournemouth in 2016-17, last featured for the Three Lions in their surprise Euro 2016 defeat to Iceland last summer.
Wilshere stood out for Arsenal in their recent Europa League win against BATE Borisov, though he has yet to play a single minute in the Premier League this term.
Following another abject team display against Slovenia on Thursday, there have been suggestions in the British press that Southgate is ready to turn to Wilshere for next month's friendlies against Germany and Brazil.
Probed on the issue on Saturday afternoon, the England manager told reporters: "Everyone knows the quality Jack has. But he's got to be playing regularly. He has the quality to play at highest level."