Swansea are believed to have enquired after the towering midfielder as they consider replacements for Icelandic playmaker Gylfi Sigurdsson. The former Spurs midfielder is widely expected to leave this summer and has been heavily linked with a move to Everton.
Denmark youth international Billing made 28 appearances for the 'Terriers' in all competitions last season, but made just 13 starts in the Championship as David Wagner's side earned promotion through the play-offs.
It had been suggested that the Yorkshire side would consider selling the 21-year-old for a fee in the region of £10m but 'The Daily Mail' reports that this is not the case, with David Wagner believed to have high hopes for the player this season.