England winger Hudson-Odoi is yet to feature in the Premier League for Chelsea this term, despite starting the UEFA Super Cup penalties victory over Villarreal.
German giants Dortmund are keen to bring in the 20-year-old and deploy him in his favoured left-wing role, the PA news agency understands.
Hudson-Odoi has been determined to push for regular first team action at Chelsea under first Frank Lampard and now Thomas Tuchel.
Former Paris St Germain boss Tuchel has used Hudson-Odoi as a wing-back in his 3-4-3 system at Chelsea.
While the 48-year-old Blues manager remains a vocal fan of Hudson-Odoi's attitude and his quality, he has also conceded the young England star could find his path blocked to an advanced left-sided role in west London.
Tuchel insisted on Friday that there was no loan scenario for Hudson-Odoi at that stage, but the final throes of a transfer window are always changeable.
Kurt Zouma's £25million departure to West Ham has opened a space in defence that Chelsea still hope to fill with the recruitment of Sevilla's France star Jules Kounde.
A loan swoop for Atletico Madrid's Saul remains another possibility for the Blues, with one slot in defensive midfield still vacant after Billy Gilmour's season-long loan move to Norwich.
The Blues later confirmed that Tiemoue Bakayoko has rejoined AC Milan on a two-year loan.
The midfielder's second spell with the club is due to run until 2023. He previously played for the club in 2018-19 and also spent last season with Serie A rivals Napoli.