The Blues have long been considered the favourites to sign Rice, who previously spent time in their academy system.
Rice was rumoured to be close to joining Chelsea last summer, but the West London outfit could not justify splashing out more money after spending £120m on other players.
According to 90min, Chelsea are still interested in signing the England international, though they now face competition from at least three other teams.
The same report indicates that Chelsea and City consider Rice more of a centre-back, whereas Liverpool and Man United intend to keep him in his current holding-midfield position. body check tags ::