It was revealed earlier in the week that several Championship clubs are keeping tabs on Haynes, who has impressed since joining the Tykes from Bristol City in January.
The likes of Burnley, Hull City, Leicester City and Portsmouth are all understood to be monitoring the 23-year-old's situation at Oakwell.
However, Barnsley director Don Rowing is adamant that Haynes, who is under contract until 2013, is not for sale.
"There's absolutely no truth in these rumours, we have no intention of selling Danny Haynes," Rowing told the Sheffield Star.
"We've had no official approaches from Burnley or any other club for Danny. He's got two more years to run on his contract and is a Barnsley player.
"I really don't know where these rumours come from sometimes, but that's exactly what they are - rumours."
Source: Team Talk
Source: Team Talk