The 26-year-old has impressed with his exploits in the Championship last season as he played a big role in helping the club to retain their status on their return to the second-tier.
Yiadom joined the Tykes on a free deal at the start of 2016-17, having previously spent time lower down the football ladder with Barnet, Braintree Town and Hayes and Yeading United.
The full-back turned out 33 times in all competitions last term with his opportunities restricted due to a shoulder injury.
Swansea boss Paul Clement is keen to enhance his squad for the 2017-18 campaign and reports claim Yiadom will be a key part of that.
It’s understood the Ghana international, who represented his nation at the 2017 Africa Cup of Nations, could be available for around £2million.