The 21-year-old joined Chelsea from Sporting CP last year but was troubled by injury for much of his debut campaign, limiting him to a handful of appearances.
According to journalist Ben Jacobs, Chelsea are open to sending the Portugal Under-21 international out on loan for the season, with promoted Hull City among the suitors, alongside Ligue 1 side RC Strasbourg, who share ownership with Chelsea under the BlueCo group.
Any move is expected to be a straight loan without an option to buy, reflecting Chelsea's continued belief in Essugo as part of their long-term midfield plans despite the growing competition for places under Xabi Alonso.
The arrivals of Jordan Henderson and Valentin Barco this summer, along with the emergence of academy players, have left limited opportunities for Essugo at Stamford Bridge for now.
Essugo has shown promise in the minutes he has managed to get on the pitch, and a temporary move would give him the regular football he has been missing since his move to west London. He remains under contract with Chelsea until the summer of 2033.