The young England star could find his path blocked to an advanced left-sided role with the Blues.
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.