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The Premier League club, who currently sit just one point above the top-flight’s relegation zone after back-to-back league defeats to Arsenal and Swansea City respectively, have been linked with luring the Arsenal right-back to Selhurst Park this month.
The 24-year-old, who has one cap for the Three Lions after making his senior international debut against Sweden back in November 2012, has made just five first-team appearances for the Gunners so far this season.
Jenkinson, who was loaned out to Premier League rivals West Ham United during the 2014-15 and 2015-16 campaigns, has 18 months remaining on his current deal at the Emirates Stadium.
However, the report suggests former loanee side West Ham, Watford, Swansea City and Championship club Aston Villa are also interested in Jenkinson’s services.
New Eagles boss Sam Allardyce was initially eyeing a loan move for the full-back, although he now believes he can sign the defender on a long-term deal.