Tottenham and Chelsea are among the clubs reported to have been told Ben Gibson would cost £25m.
The Daily Star say Middlesbrough have told clubs interested in the defender that they will not sell him on the cheap.
Those clubs are said to be Chelsea, Spurs, Everton, Leicester, Southampton and Stoke
Meanwhile, Tottenham are ready to instigate contract talks with Toby Alderweireld, the Daily Mirror say.
The Belgian defender has two years left on his current deal and there has been speculation about his future.
According to reports, he earns £50,000 a week at Spurs and wants to double that, which would apparently mean parity with the likes of Harry Kane and Hugo Lloris.
Inter Milan, seemingly keen to spend heavily in the transfer market following the arrival of Chinese investors, have been linked with Alderweireld in recent months.
The Mirror say Spurs, who have an option to extend his contract by 12 months, have no intention of letting him leave the club.
The Mirror also say John Terry is ready to sign for Aston Villa when his Chelsea contract expires at the weekend.
And Tottenham are interested in Southampton right-back Cedric Soares, again according to the Mirror.
Soares has been touted as a possible replacement for Kyle Walker, who has been tipped to leave.