The 25-year-old has struggled to cement himself a regular spot in Arsene Wenger’s starting XI this season, making just one Premier League appearance.
Jenkinson has been with the Gunners since 2011, but has managed just 38 league showings to date for the north London outfit.
Carl Jenkinson came close to joining Crystal Palace last month
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I think in a number of ways, Palace would have been a good fit
Sam Allardyce, who Jenkinson played under at West Ham, was keen to have him at Selhurst Park to address his defensive concerns at right-back.
And even though a deal never materialised, Jenkinson admits he considered making the move south.
“I think in a number of ways, Palace would have been a good fit,” he told The Telegraph.
“It would have enabled me to play again and that’s all I want: to play football.
Sam Allardyce was keen to reunite with Carl Jenkinson at Selhurst Park
Carl Jenkinson Has made just one league appearance for the Gunners this season
“I had a great year with Big Sam [Allardyce, at West Ham], played some of the best football of my career and got on very well with him.
“I’ve got great respect for him as a manager. The opportunity to play under him again was something I was interested in doing. In the end it didn’t pan out.”
Jenkinson is still under contract with the Gunners until 2018.