The Wales international defender could be set to leave his hometown club to link up with former Magpies boss Alan Pardew at Selhurst Park.
The 23-year-old is yet to feature this season after a hamstring problem ruled him out of the opening batch of Premier League games. Dummett was on the bench for the League Cup win over Northampton Town.
The report claims former Magpies boss Alan Pardew is a big fan of a player that he gave a debut to during his spell at the club. Adding a little more depth at left back is something that the Eagles have been eager to do this summer, but the Chronicle have said that there was a desire to get some squad players off the wage bill before they brought in further additions.
Recent departures of Barry Bannan and the impending sale of Glenn Murray to Bournemouth have freed up some room in that regard, meaning a transfer could be on the cards.
Papa Souare and Martin Kelly are the club's options at left fullback, though the former Liverpool man is traditionally a right back. The Senegal international has been in good form, but there is an opportunity to add another face there, with Zeki Fryers failing to convince since moving from Spurs.
The Chronicle have said that the Magpies rate Dummett, who has two years on his contract, at £8 million. With a bid still to be tabled, time is running out for Pardew if he decides he wants to bring the defender in.
Many of Dummett's 51 matches for his hometown club came under the 54-year-old, and the Wales international could be given the chance to continue his career under Pardew with a move to London.