According to BBC sport report, the 19-year-old striker enjoyed a productive loan spell with Bristol City last term, where he scored 26 goals in 48 appearances across all competitions.
His exploits in the Championship for the Robins are believed to have drawn the attentions of Newcastle and Brighton, with the Swans also joining the chase for Abraham.
Huw is hoping the lure of former Blues coach Paul Clement will count in their favour, after he previously worked with the teenager at Stamford Bridge.
"He's a young and up-and-coming player we are interested in," Huw told BBC Wales Sport. "Tammy does not have Premier League experience, but we are interested.
"Paul knows him from Chelsea. If you look at the options which have been publicised, (they are) Brighton, Newcastle and ourselves, so it is left to Tammy and his family to decide where he wants to go next."