The Black Cats have agreed a deal worth around €4m (£3.4m) for Ellborg, with the shot-stopper having been given permission to travel to England to complete the move.
A medical has been arranged, and provided there are no unforeseen issues, Ellborg's transfer should be completed within the next 24 hours or so.
That will pave the way for Sunderland to sanction Patterson's departure, with Millwall heading a queue of clubs keen to secure the signature of last season's promotion winner.
Ellborg joined Malmo as a teenager and signed his first professional contract in 2020 after impressing in the UEFA Youth League.
He has had loan spells at IFK Malmo, Ariana and Trelleborgs, and made his Swedish top-flight debut last May in a 3-0 win over Hallstads.
He has made seven top-flight appearances for Malmo, and has been capped by Sweden to Under-19s level.
He is set to become the most expensive goalkeeper in Swedish Allsvenskan history, with his transfer fee exceeding the one that was paid by Brentford to sign Hakon Rafn Valdimarsson from Elfsborg in 2024.
Sunderland have also been linked with a potential move for Chelsea forward Tyrique George in the final three days of the transfer window.