Owen Coyle is an admirer of Williams, who played in a number of positions last season during Boro's successful end to the Championship campaign.
The Trotters boss is reportedly prepared to allow young prospect Mark Connolly to join Boro on a season-long loan in order to seal a deal for the defensive pair.
Coyle first inquired about Williams at the end of the season, but Boro boss Tony Mowbray had indicated that there was no real need to sell players who will form a major part of his starting XI this season.
However, the offer of former Wolves player Connolly who Bolton signed for £1million 18 months ago may tempt Mowbray, who is understood to have watched the youngster play for Bolton's reserve team on a number of occasions, to part with Williams and Hines.
Williams made ten appearances for Boro at the back end of the season after returning from a pelvic injury which ruled him out for 11 months.
Hines, who replaced David Wheater in Boro's starting line-up after his January move to the Trotters, could be reunited with his former team-mate.
Mowbray has confirmed that striker Kris Boyd is in talks with Turkish club Eskisehirspor.
The 27-year-old, who spent the end of last season on loan at Nottingham Forest, travelled to Turkey as Boro attempt to slash their wage bill.
Mowbray said: We have allowed him to go and have a look and if he's happy with everything, potentially have a medical. That doesn't mean it's done, there are lots of things that need tidying up. If it's right for Kris and our football club, we will wish him well and move on.
If not, he comes back and tries hard to get in our team and hopefully he will start scoring goals like we know he can.
Boyd joined from Rangers last summer, but struggled to reproduce his form north of the border at the Riverside.
His return of six goals in his maiden season on Teesside was not enough to endear himself to the Boro fans, and a series of ineffectual performances in attack drew the ire of a number of supporters.
It is understood that Eskisehirspor are offering £15,000 more after tax than he currently earns at Boro.