The 28-year-old is currently under contract at Leeds United but has already travelled to Austria and trained individually with Schalke's squad at their pre-season camp, before passing a medical.
According to multiple reports, Wöber will move to Gelsenkirchen on a free transfer once his Leeds contract is mutually terminated, and is expected to sign a performance-related deal with the Bundesliga club.
The centre-back spent last season on loan at Werder Bremen but managed just three appearances because of injury, meaning Bremen did not take up their €4m option to sign him permanently. His most productive spell in Germany came during a loan at Borussia Monchengladbach in the 2023-24 season, where he made 25 Bundesliga appearances and scored twice while operating both in central defence and at left-back.
Wöber's contract at Leeds, where he has been since 2023, was due to run until next year, but the two parties have agreed to part ways to allow the move to Schalke to go through as a free transfer.
With Wöber's arrival now expected, Schalke look set to move on from their interest in Felix Uduokhai. The 28-year-old left-sided centre-back, who is currently with Besiktas, had also been strongly linked with a switch to Gelsenkirchen, but Wöber's imminent arrival appears to have ended that particular pursuit.
Wöber, who came through the Rapid Wien academy before spells at Ajax, Sevilla and Red Bull Salzburg, joined Leeds in January 2023 and has made 31 senior appearances for Austria. Injuries have disrupted his career in recent years, including a thigh problem that wrecked much of his time at Werder Bremen and forced him to miss Austria's involvement at this summer's World Cup.
According to reports in Germany, Wöber is set to sign a two-year contract at Schalke, giving the newly-promoted Bundesliga club another experienced option at the back as they prepare for their return to the top flight following last season's promotion.
Schalke finished top of the 2. Bundesliga table last season under head coach Miron Muslic, securing an immediate return to the Bundesliga following their relegation in 2023. Adding a defender with Wöber's experience of the division is seen internally as a low-risk way to shore up a defence that will face a step up in quality this season.