The 29-year-old said he might have joined Arsenal had he not been involved in Gervinho's red card on the opening day of the season while playing for his former club, Newcastle.
He clashed with the Gunners' new signing at St James' Park, going to ground after a fracas which saw the Ivorian sent off.
Barton believes that incident was pivotal in Wenger deciding against bringing him to Emirates Stadium.
However, Arsenal chief Hill-Wood says he had no knowledge of the manager trying to sign the tempestuous midfielder.
He told the Daily Star: "It's not something the board heard about and if it was a serious proposition I certainly would have expected us to."