The 22-year-old midfielder is currently on loan with MK Dons in the Championship, and the Swans went out to scout him over the weekend when he made his debut for the club in a 3-1 loss to Bolton Wanderers.
Williams is set to stay with the Dons until the end of this season, and Swansea will continue to track the midfielder for the rest of the year ahead of making a move for the Welsh midfielder in the summer.
The Premier League side are said to be keen on the pair, and a ready to make a £2 million offer for them this month.
They have been watched by the Welsh club a number of times in recent months, and the £2 million offer will include a number of add-ons relating to appearances and Premier League placing.
It is not known whether Bolton are ready to accept the offer, although their financial status might make accepting a bid a necessity.