Chelsea are prepared to offer Barkley to West Ham in order to land Rice from the Hammers, reports Football Insider.
The Blues are set to submit a bid in their pursuit of the England midfielder that will include Barkley and cash.
Chelsea value Barkley at £30 million and are willing to let the 26-year-old leave this summer.
He has three years remaining on his contract but is behind Havertz and Mason Mount in the attacking midfield pecking order.
West Ham, however, value Rice at £80 million and are hesitant to sell for anything less than that price.