The defender has never made the grade at Arsenal and boss Unai Emery is prepared to cash in on him.
Arsenal are currently attempting to sign Eagles star Wilfried Zaha.
But their opening bid of £40m has been laughed at by Palace, who value the winger at double that amount.
After two years of missing out on Champions League cash, the Gunners are financially hamstrung.
And Emery is willing to sell Jenkinson to bring in a much needed £5m transfer fee and get him off the wage bill.
Arsene Wenger signed the right-back from Charlton for around £1m in 2011.
But after Hector Bellerin’s emergence, he has been generally restricted to the role of backup.
Loan spells at West Ham and Birmingham in the Championship illustrated that he was not of Arsenal calibre.
The Sun report that Palace are interested bringing Jenkinson in as a replacement for Aaron Wan-Bissaka.
The Selhurst Park outfit sold the youngster to Manchester United for £50m last week.
Eagles boss Roy Hodgson has always been a fan of Jenkinson since his days as England manager.
He even gave the 27-year-old his England debut against Sweden in 2012.
Emery is looking to save money by loaning out Mesut Ozil as well, as the likes of Shkodran Mustafi.
The Spaniard’s hopes of signing Zaha were boosted yesterday by the Ivorian’s brother’s comments.
“It’s my brother’s dream though to play for Arsenal,” said Zaha’s brother Judicael.
“I hope Palace will be able to see their way to agreeing a deal with Arsenal that allows Wilfried to realise his dream of playing European football for the club he’s supported since childhood.”