Rice was heavily linked with the Blues last summer, but they could not negotiate a deal with West Ham United after already spending £225m on seven players.
According to The Express, the west London giants will return for the England international this summer with new manager Thomas Tuchel interested in signing him.
The club are unlikely to afford the reported £80m price tag, but they will look to drive down the overall valuation by negotiating a player-plus-cash deal with the Hammers.
They are prepared to offer Abraham, Loftus-Cheek or Christensen as a makeweight to pursue Rice. Abraham could be the realistic target for the Hammers as they have only one specialist striker.