Rushworth, 23, joined Coventry on loan from Brighton last summer and has been a consistent presence in Frank Lampard's side throughout the promotion campaign. Newcastle United sent scouts to watch him with a view to a summer move, but Coventry's established relationship with the goalkeeper and the direct working bond he has built with Lampard appear to have given the newly-promoted side a decisive advantage.
A permanent deal would need to be agreed with Brighton, who signed Rushworth from Halifax Town in 2019 after he turned down approaches from Arsenal and Manchester United.
He came close to a call-up to Thomas Tuchel's England squad in March and remains in contention for international recognition if his form continues into the Premier League.
The signing is expected to be the first of an aggressive Coventry summer window. Lampard has acknowledged the urgency of strengthening the squad quickly, and the club are also working on a permanent deal for striker Frank Onyeka, who joined on loan earlier in the campaign.