Brendan Rodgers is understood to have had a spy in place at Oakwell for the Tykes' 1-1 draw with Norwich City on Tuesday night.
And with the one-time Ghana international Yiadom refusing to sign a new deal with the South Yorkshire club, Celtic can move in and take him on a free transfer in the summer.
Right-back is one of Rodgers' top priorities ahead of the summer transfer window with Mikael Lustig having struggled at times this term.
Anthony Ralston performed well earlier this season but was ignored in favour of Kristoffer Ajer at right-back in the recent Old Firm derby.
And the Daily Record has suggested Yeovil Town's 21-year-old Tom James is another target for the summer transfer window.
Huddersfield Town were interested in Yiadom last summer but pulled out in August, while Swansea City launched a deadline-day bid for the 26-year-old to no avail.