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He played a key role as the Yorkshire side won the League One play-offs to win promotion to the Championship.
And it is no surprise that the club flatly rejected the Shrimpers' bid of £100,000 for the player - especially with United owed a percentage of any transfer fee they receive for him.
"We're not even considering their offer," said Barnsley manager Andy Ritchie.
"It's no where near our valuation of him and he will not be going any where.
"I value Paul highly and paid good money for him last summer."
Southend boss Steve Tilson will have been keen to link Hayes with Freddy Eastwood, after rejecting a £1million bid from Derby County for the striker who finished top scorer in League One last season.