It is unclear whether or not the Crystal Palace winger will become a permanent Huddersfield Town player.
The newspaper claims Puncheon has 'headed to Yorkshire to complete a deal (that will run) for the rest of the season'.
The 32-year-old is in the final six months of his Crystal Palace contract and has played just eight times in league and cup this campaign.
His rumoured arrival at Huddersfield would proceed the sale of another winger, Rajiv van La Parra, to Middlesbrough.
Puncheon has spent the past five-and-a-half years at Crystal Palace, whom he initially joined on loan from Southampton.
The Croydon native has also had Premier League spells with Blackpool and Queens Park Rangers and counts Wimbledon, Milton Keynes Dons, Barnet and Plymouth Argyle among his other clubs.
Both Crystal Palace and Huddersfield are in a fight for survival at the bottom of the English top flight this season.
Is Puncheon a good addition for David Wagner's Terriers?
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