Gray left the Clarets for Watford earlier this month so Walters, who joined in a £3million deal from Stoke earlier in the summer, is expected to start against the champions in the opening round of fixtures.
Fellow summer captures midfielder Jack Cork and full-backs Charlie Taylor and Phil Bardsley will also be pushing for debuts at Stamford Bridge.
Burnley also lost defender Michael Keane to Everton over the summer and manager Sean Dyche accepts it is a blow to no longer have Keane and Gray at his disposal, but he is confident others within his squad will step up and fill the void.
"No-one wants to lose their best players, but there's a reality to all clubs, particularly this one," he said.
"There's still a level this club operates to. It makes it tough at times, but it's the reality.
"Some outgrow the club financially. When these opportunities come around, they're there to be gripped by the players, so there are obvious slots available."