The 24-year-old, who replaced Mark Noble as Hammers captain last summer, has spent his entire senior career with the East Londoners, scoring 14 goals and providing 13 assists in 240 games across all competitions.
Rice has established himself as a key player for both West Ham and England, but he has been strongly linked with a departure from the London Stadium for some time, with his contract set to expire in the summer of 2024.
The Hammers were vying for Europa League silverware last season before finishing seventh in the Premier League, but they have since endured a decline in fortunes on the domestic front this campaign and are set for a bottom-half finish in the top flight, albeit remaining in the mix to win the Europa Conference League.
Rice revealed earlier this season that he is keen to fulfil his dream of playing in the Champions League, sparking speculation over a big-money move to the likes of Arsenal, Manchester United, Manchester City, Liverpool and Newcastle United, who have all been credited with an interest.
Moyes have consistently expressed his desire to keep hold of Rice, who is valued by the Hammers at around £100m, but the Scotsman has since acknowledged for the first time that the midfielder could leave the club this summer.
Speaking at a press conference on Friday ahead of Sunday's Premier League trip to Brentford, Moyes said: "We honestly hope [Rice] stays. We'd love for him to be a West Ham player but we are aware that might not be the case at the end of the season.
"So that's one of the scenarios around planning. There are plans that we have Dec here but we're also fully aware there is a good chance we won't have him."
Moyes has admitted that West Ham have been unable to put together transfer plans for the new season while their Premier League status remains uncertain, although after several months of being embroiled in a relegation dogfight, the Hammers are now on the verge of securing their top-flight status, sitting seven points clear of the drop zone.
"The planning has been put on the back burner. It's always been about making sure you're a Premier League club," Moyes added. "Your planning will go completely if you weren't.
"A lot of it will only start to go into place once we've realised we have kept our Premier League place. We're watching a lot of players, a lot of games, doing a lot of scouting, but the truth is the focus has been on staying in the Premier League."
Premier League title challengers Arsenal are believed to be the current frontrunners for Rice's signature, with Mikel Arteta allegedly confident of luring him to the Emirates Stadium this summer.
A recent report claims that Arteta will received a £150m summer transfer budget from the Gunners hierarchy, although a significant chunk of that would seemingly be needed to tempt West Ham into selling Rice.
The 41-cap England international could be regarded as a potential replacement for Granit Xhaka who is reportedly attracting interest from Bundesliga club Bayer Leverkusen.
Man United are also said to be firmly in the race to recruit Rice, with manager Erik ten Hag identifying the box-to-box midfielder as his number one summer target.
Man City, meanwhile, may consider stepping up their interest in West Ham's No.41 now that they are allegedly resigned to missing out on Jude Bellingham, who looks increasingly likely to join Real Madrid this summer.