The Scot has been the subject of speculation regarding his future over the past year with his performances having attracted interest from a number of Championship clubs including Stoke, Derby, West Brom and Brentford.
SPL champions Celtic have also been keeping tabs on Lindsay, while Italian outfit Brescia are also known admirers.
The Serie B champions - whose president is former Leeds United owner Massimo Cellino - have been linked with Lindsay since last summer.
But the Potters have made a decisive move to sign Lindsay, with national reports stating that a deal worth over £2 million has been agreed, with the player to undergo a medical later this week ahead of finalisation of the transfer.
Lindsay has a year left on his current Oakwell contract, with the club having made overtures to the player regarding fresh terms.
Like Lindsay, several other leading players see their deals expire next season, including Ethan Pinnock and Cameron McGeehan.
Should Lindsay complete a move to the Potteries, he is likely to be joined by Reds keeper Adam Davies, who is expected to complete a move to Stoke by the end of the month, when his Oakwell deal expires.
On the incoming front, the Reds have a number of targets who they are actively pursuing.
So far this summer, the club have completed two incoming deals, with highly-rated Derby County winger Luke Thomas signing for Barnsley for an undisclosed fee last week, with the 20-year-old penning a four-year deal.
The Oakwell outfit have also signed former loanee Mike-Steven Bahre on a permanent basis from Hannover following his successful loan at the club last season.