Walsall are searching for a new manager after Dean Smith left the Bescot Stadium to take over at Championship side Brentford earlier this week.
A number of names have been linked with the Walsall vacancy, but former West Brom defender Moore is thought to figure highly on the club's wanted list.
John Ward, John Whitney and Neil Cutler are in tempoarary charge at Walsall until the club bring in a new manager.
Moore is highly-rated in coaching circles and although he primarily works with West Brom's under-18 and 21 sides, he is also part of Tony Pulis' first-team staff.
Moore is currently in his second spell coaching at West Brom after initially taking up a role with the youth team after hanging up his boots in 2012.
The 41-year-old left West Brom in January 2013 to become first-team coach at Blackburn Rovers alongside former Baggies team-mate Michael Appleton, but he returned to West Brom in September 2014.
Moore is thought to be interested in moving into management in his own right and he knows a few of the Walsall players already having worked with the likes of Romaine Sawyers and Sam Mantom when they were coming through the West Brom academy.