The 22-year-old was heavily linked with a move away from West Ham during the recently concluded transfer window, but is still at the club.
Chelsea were credited with an interest in signing Rice, while Manchester City and Manchester United were also said to be keen.
However, West Ham’s valuation of £100m and other reasons saw Chelsea, Manchester City and Manchester United turn their attention elsewhere in the summer.
Rice, though, remains of interest to the Premier League trio and is expected to be at the centre of a three-way tussle between them next year.
The England international has high expectations for his career and there are suggestions that this is likely his last season at West Ham.
If Rice is keen on a move next year, Chelsea, Manchester City and Manchester United are all expected to push to acquire his services.
Jurgen Klopp’s Liverpool could also join the mix to make it a four-way tussle for Rice.