The 24-year-old is widely expected to leave the London Stadium during the upcoming market, and a number of Premier League clubs are thought to be considering making a move.
Arsenal continue to be heavily linked with the England international, while Manchester City, Manchester United and Liverpool are also being credited with an interest ahead of the summer market.
Talk of a potential return to Chelsea has quietened in recent months, with the Blues spending heavily on Enzo Fernandez during the January transfer window.
However, according to German journalist Florian Plettenberg, Graham Potter's side are 'definitely in the race' for the Englishman, who is viewed as one of the club's leading targets for the summer.
Rice has again been an important player for West Ham during the 2022-23 campaign, scoring twice and registering four assists in 34 appearances in all competitions.
The midfielder's existing deal with the Hammers is due to expire in June 2024, although the club have the option of activating a one-year extension to take him until 2025.
Rice is widely expected to be on the move this summer, with David Moyes's side believed to be looking for a fee in the region of £100m.
The Englishman spent seven years in Chelsea's academy system before being released at the age of 14, moving to West Ham shortly after.
West Ham sporting director Mark Noble recently admitted that Rice could leave the London Stadium in the near future to realise his dream of playing in the Champions League.
"Wherever Declan ends up, or however much someone pays for him, whether it's here or anywhere else, he's worth every penny," he told the Evening Standard.
"He's said openly he loves playing at West Ham, but he has got ambitions as a player to go and play in the Champions League and win trophies.
"I don't think any West Han fan can actually have an agenda over that. Do you blame him for having really big ambitions? Of course you don't. If he didn't, he probably wouldn't be as good as he is."
While speaking to reporters at the 2022 World Cup, Rice revealed that he '100% wanted to play in the Champions League' in the near future.