Manchester United manager Louis van Gaal has refused to rule out the possibility of signing goalkeeper Victor Valdes.
Manchester City boss Manuel Pellegrini says he is confident that England goalkeeper Joe Hart will sign a new contract.
Huddersfield are holding firm over their valuation of the former Leeds and Manchester City man, despite Clayton having just 12 months left on his current deal.
The 25-year-old has become an integral part of the Town set-up since joining from Leeds in 2012, and he has been the subject of a number of bids this summer, with Boro and Brighton both having offers rejected.
The two clubs are continuing dialogue with Town, but they also have other targets they are progressing with.
Town's signing of Radoslaw Majewski on loan from Nottingham Forest this week has encouraged both Boro and Brighton further that they can prise Clayton away from the John Smith's Stadium.