Conte's future at Stamford Bridge has been the subject of intense debate throughout the course of the season, with the Blues surrendering their Premier League title and on course to finish outside the top four.
The Italian has regularly clashed with the Chelsea board and looks increasingly likely to move on at the end of the campaign, despite leading the club to the title in record-breaking fashion during his debut campaign in English football.
The Daily Star reports that Nagelsmann has emerged as a surprise candidate to replace Conte in the dugout following his impressive work with Hoffenheim over the past two seasons.
The 30-year-old - who became the youngest manager in Bundesliga history when he took over at Hoffenheim in 2016 - saved the club from relegation in his first season at the helm before remarkably guiding them into the Champions League for the first time in their history in 2016-17.
Hoffenheim are on course to repeat that feat again this term and will be guaranteed another top-four spot if they win their final two games of the season.
Nagelsmann is currently contracted to the club until 2021 and has a release clause that does not become active until next summer, but Roman Abramovich is reportedly considering trying to prise him away from the German outfit.
Chelsea had initially been linked with Luis Enrique and Massimiliano Allegri, but they were reportedly put off by the former's financial demands, while the latter is thought to favour a move to Arsenal.