Rice looks set to step down this summer after 16 years as the Frenchman's number two due to a chronic knee problem.
Wenger praised his long-serving assistant and also revealed that Bould is one of the prime candidates should Rice make his retirement official.
"It looks like [Rice] could stop, but it is not official yet," said the 62-year-old. "Pat is fantastic. He works every day hard and never speaks to the Press - fantastic!
"It is possible [Bould will get the job]. Everywhere I go I keep somebody who knows the club and worked inside the club, so it is a possibility."
Former Arsenal defender Bould, who is the current youth team coach at the North London club, was part of the Gunners' playing staff between 1988 and 1999.