David Wagner is in advanced talks with Schalke over the vacant manager's job, according to Sky in Germany.
Wagner left his role as Huddersfield head coach on mutual terms earlier this season, replaced by Jan Siewert, after leading the club to an unlikely Premier League promotion in 2017 and defying the odds to survive relegation in 2018.
Sky Sports News understands fellow Bundesliga club Hertha Berlin are trying to rival Schalke for Wagner's signature, but no formal offers have been made and the 47-year-old is considering his options.
Schalke reached the Champions League last 16 this season where they lost 10-2 to Manchester City over two legs and have struggled domestically in Germany, sitting 15th after 31 top-flight games.
The club finished second last term under Domenico Tedesco, who was dismissed after losing to City, with Wagner one of three candidates considered - along with Borussia Monchengladbach's Dieter Hecking.
Schalke first approached Wagner a few weeks ago - when the 47-year-old said he was not ready to return to football - but negotiations have now resumed and reached the final stages, with an appointment expected next week.
Wagner, born in Germany but represented the United States at international level, played for Schalke from 1995 to 1997 and won the UEFA Cup during his time at the club.
Schalke are also in the hunt for RB Leipzig's top-rated English sporting director Paul Mitchell, who is wanted by Manchester United, Chelsea and Arsenal, Sky Sports News understands.
Mitchell was previously head of recruitment at Tottenham and Southampton - responsible for bringing Dele Alli, Toby Alderweireld and Kieran Trippier to Spurs - as well as discovering Sadio Mane and Dusan Tadic for the Saints.