The 18-year-old is believed to be on his way out of the club after turning down contract extension.
However, there are reports the youngster could sign a permanent contract after several persuasions after being handed his first Premier League start against Brighton last week.
The Ghana-born England international followed up with another start against West Ham United as fears grows over his future.
Chelsea manager Maurizio Sarri gave him a chance after chance after he was capped by England.
But Liverpool legend Jamie Carragher is unimpressed and wants the winger to turn down a new deal.
Carragher told Sky Sports: ‘If I was Hudson-Odoi, I wouldn’t sign. He’s in a strong position. I wouldn’t sign to get more money or cause drama. He wants to play and I love the courage he’s show.
‘Youngsters sign big long contracts and you wonder, where the career is going but he’s willing to say, “I want to go”.
‘I would use the last year of my contract as leverage. He wants to play and he wants to show Chelsea what he can do. I’ve got great respect with what this lad is doing.