But amid the transfer talk, Rice celebrated his 100th Premier League appearance for current club West Ham last weekend.
And Hammers co-owner Gold has congratulated the young midfielder on the achievement, perhaps signalling any move to Chelsea is not particularly close.
“I would like to congratulate Declan on his 100th Premier League appearance for West Ham United – a magnificent achievement,” Gold said on Twitter.
“I am very proud of him and he epitomises everything that this great football club stands for.”
Rice also celebrated the landmark, saying: “Not the result or performance we wanted last night, but a very proud moment to have made my 100th premier league appearance. Hopefully many more to come.”
Rice has been with West Ham since 2014 when he joined from Chelsea, who released him aged 14.
He is now being heavily linked with a return to Stamford Bridge, but it won’t come cheap with the Hammers valuing their England international at £70million.