The Ghana international joined the Tykes last summer but looks set to leave after just one season with plenty of clubs expressing an interest.
Newly promoted Huddersfield are known to be big admirers of the 25-year-old, although Swansea and Reading are also keen.
Reports claimed last week that the Terriers had given up on signing the former Barnet man but Yiadom is now understood to have told Barnsley he wants to move on.
Yiadom has played the full 90 minutes in Barnsley's first two games of the new campaign against Bristol City in the Championship and Morecambe in the Carabao Cup.
However, he may not feature again for the Tykes and Huddersfield are expected to return with a third offer in the region of £2million.