The 22-year-old joined the Gunners back in 2011 and has since enjoyed loan spells at Lorient, Betis and Olympiakos.
He impressed with Costa Rica at the World Cup and is thought to be interesting AC Milan amongst others.
However, Wenger insists the striker is not going out of the club again on loan, telling the Sunday People: “We have had a lot of offers for Joel and have turned them all down.
“There are plenty of clubs – I don’t know exactly how many because once I said to my assistants, ‘He will not go out on loan’, if somebody calls them they don’t even tell me anymore because, when I say no, it’s no.
"But he is definitely a player wanted by many clubs.”