Flitcroft was relieved of his duties following Saturday's 3-0 home defeat to Birmingham, which left the Tykes bottom of the Sky Bet Championship table, six points adrift of safety.
Wilson has now been backed into odds-on for the vacant position with Sky Bet, with the online bookmaker reporting overwhelming support for the 54-year-old to return for a second spell in charge, having started his managerial career at Oakwell almost 20 years ago.
Michael Appleton was installed as the initial favourite but has drifted out to 5/1, while Neil Redfearn, Mike Phelan and Steve Agnew are considered the other possible options at 16/1 apiece.
Sky Bet Football Trader Chris Spicer said: "We've seen almost 80 per cent of stakes on Wilson taking the job with very little interest in any of the other candidates.
"Saturday's hefty defeat prompted us to cut their relegation odds from 4/6 to 4/9, having started the season at 2/1, so it looks a tough task for whoever takes the job to keep them up."