The 23-year-old Australian defender/midfielder has been the subject of Bolton's advances in the past with manager Owen Coyle known to be an admirer of his, from their time at Burnley together.

Boro had previously turned Bolton's moves for Williams and have once again rejected their bid according to Sky Sports, with the financially-troubled club steadfast on retaining their key players as they bid for promotion.

Bolton are believed to be keen on signing a new defender following the sale of England international Gary Cahill to Chelsea.

Williams, who has reportedly attracted attention from Liverpool, Newcastle and West Brom, has made 28 appearances in all competitions this term for Boro.

The Perth-born utility's return to fitness in March last year coincided with Boro's upturn in results as they went from relegation battlers to promotion contenders.

Williams' current contract with Middlesbrough expires in June 2013.