Jones is out of contract at Kilmarnock at the end of the season, and Swansea in the Championship in England reportedly want to secure the services of the Northern Ireland international midfielder in the January transfer window.
According to The Daily Mail, Aston Villa in the Championship in England have also been monitoring the progress of Jones.
Jones is one of the best players in the Scottish Premiership and is a key figure in the current Kilmarnock team.
The former Middlesbrough prospect has provided three assists in 11 Scottish Premiership appearances for Steve Clarke’s side so far this season, according to Transfermarkt.com.
Jones would be a good signing for Swansea or Villa in their respective quest to finish in the top six of the Championship this season.