Premier League giants Manchester United and Chelsea have long been linked with the flourishing England international, who has helped the East London side to the brink of qualification for the Champions League.
The Hammers are currently fifth in the table, with Rice an integral part of the side who are also still involved in European competition.
Only attacker Jarrod Bowen currently ranks higher than 23-year-old Rice on the Opta-stats-powered website WhoScored.com, which measures individual player performance from match to match.
The former Chelsea youth player was named as the Young Player of the Year at the London Football Awards in 2019 and was recognised again this week, as he discussed what keeps him at the London Stadium and more.
After winning the Player of the Year award at the London Football Awards on Thursday night, Rice is reported as saying: “The first spell [with Moyes in charge] I was very young and was learning my trade and playing centre-half.
"Then, it was funny because when he came back for the second spell he came over and said to me 'you’ve got better, haven’t you?'
"I looked at him and started laughing and from that moment on we’ve had such a good relationship.
"The confidence he puts into me is massive and means I can go out and perform when a manager believes in me like that.
“It’s good to be regarded in that way. I wouldn’t be here if it wasn’t for the manager," he said.
However, West Ham may need to finish in the top four to retain their midfield star, despite a contract until 2024, with a club option for an extra year.
Rice, who has played every Premier League game but one for Moyes' side this season, has also explained that he wants to play in Europe's top competition as soon as possible too.
He told the Evening Standard on Thursday night that: "It is as urgent [to play Champions League football] as possible. I feel like, not only for me, that's for every young player as well.
"We are really close with West Ham at the minute and last season it was gutting to lose out on it but we are pushing," he said.
West Ham head to Anfield this weekend to face Liverpool before a trip to Sevilla in the Europa League last 16 on Thursday as the season boils down to the business end of the season.