Messi recently signed a new long-term deal at the Nou Camp with a €700m release clause.
New rules in Chinese football mean any deal would cost Hebei a staggering €1.4bn (£1.2bn).
Reports in various European news media said Hebei China Fortune, which signed Javier Mascherano from the Catalan side in January, are preparing another bid for Messi after their first move was rejected.
Hebei also signed Ezequiel Lavezzi and reports claimed the two signings were aimed at convincing Messi to join the club.
The Argentine extended his contract with FC Barcelona until 2021 recently, becoming the highest paid player in football in the process.
Hebei are reportedly determined to sign the Argentine star after he was named the most popular player among Chinese football fans last week, beating the likes of Cristiano Ronaldo and Paul Pogba.
However, the new transfer tax of 100% of the fee for overseas players introduced by Chinese football regulator may stand in Hebei’s way as it will bring total fees paid for Messi to €1.4bn.
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