The former Doncaster Rovers centre-half has emerged as a prime target for Wolves as Mick McCarthy looks to boost his squad for next season.
An initial offer was rejected earlier this month and the Royals have now snubbed a fresh approach from the Premier League club for Mills.
It is understood that Wolves have so far offered in the region of ?3million for Mills, while Reading are looking for a figure nearer the ?4million mark.
Wolves chairman Jez Moxey revealed earlier this week that it may be time for the club to move on to other targets after also struggling to agree a deal for Birmingham City defender Roger Johnson.
With Reading determined to hang on to Mills, it is understood the Championship club will now try to persuade the 24-year-old to sign a new contract at the Madejski Stadium.
Source: Team Talk
Source: Team Talk