The 25-year-old goalkeeper was a mainstay for the Gunners and England last season, but has lost his place at the club to summer signing David Raya.
Southgate has told Ramsdale he cannot promise him a place if he is not playing, raising the possibility that the keeper could consider his options in January if the situation is unchanged.
“I think longer term, we’re just going to have to see how it is,” Southgate said of Ramsdale. “I had that conversation with him in the last camp [in October]. We thought he did really well for us in Scotland.
“He’s still battling to be the No1 at Arsenal, and his profile and the way he can use the ball with his feet, we like, we think that’s important. But there is a reality as a keeper. If we get to March and he’s six months without playing regularly, then I’m never going to promise things that I couldn’t guarantee delivering. He knows that, he’s perfectly realistic about that.”