After the Hammers lost 3-0 to Brighton & Hove Albion last week, speculation has persisted over the future of Slaven Bilic with the East London outfit sitting in 16th place in the Premier League standings.
The Croatian has allegedly been assured that he will be given another two games to save his job but according to The Express, the West Ham hierarchy are already considering possible successors.
Nagelsmann has established himself as one of European football's top young managers after leading Hoffenheim to fourth place in the Bundesliga last season.
The 30-year-old was recently linked with Bayern Munich, but Nagelsmann suggested that he had no intention of leaving Hoffenheim in the near future.
During his time at the Rhein-Neckar-Arena, Nagelsmann has won 29 and lost just 14 of his 63 games in charge.