Ter Stegen is currently recovering from back surgery and may be encouraged to find a new club in January. His current contract with Barcelona runs until 2028, but the team is open to releasing him on a free transfer.
Instead, the Premier League clubs have proposed a loan-to-buy arrangement, which could allow them to acquire ter Stegen's services in the near future.
AS Monaco, who have previously shown interest in ter Stegen, may also re-enter the picture. The 33-year-old goalkeeper has been with Barcelona since his transfer from Borussia Moenchengladbach in 2014.