Brazilian club Flamengo are said to want to sign Jorginho on a free transfer this summer.
The 33-year-old Italian international is out of contract when the season comes to an end.
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While the Gunners may want him to stay, Jorginho knows he is only a squad player at the Emirates Stadium.
Brazilian outlet Globo Esporte claims he will get a tempting offer from Flamengo.
There are likely to be other European teams vying for the pass master if he becomes available.
Jorginho can already sign a pre-contract with teams outside of England this winter.