Following the club’s Europa Conference League victory over Fiorentina, chairman David Sullivan said he was “99%” sure Rice would leave West Ham this summer.
Rice has scored 15 goals in 245 games for West Ham, having made his debut in the 2016-17 season after coming through the academy.
He has been capped 43 times by England, playing in all five of their matches at last winter’s World Cup.
Arsenal, who finished second in the Premier League last season, signed Kai Havertz from Chelsea in a £65m deal on Wednesday.
