The midfielder is firmly in the sights of Sunderland boss Lee Johnson and the Black Cats have not been put off chasing his signature.
They have now gone in with a fourth offer for the 21-year-old, which is claimed to be worth over £1m, including add-ons.
Sunderland are continuing to hold talks to land the former Torquay United youth star and will hope that their new bid can do the trick and tempt Exeter to sell.
Johnson wants to equip his squad for a push for promotion in League One in the forthcoming campaign and Key featured regularly for Exeter last year.
The midfielder made 43 appearances in League Two for the Grecians, as they finished in ninth spot under boss Matt Taylor.
Key had a series of loan spells away from Exeter before establishing himself in the first team and is likely to be tempted by the prospect of joining Sunderland.
He has another two years left to run on his current contract at Exeter.
