The Costa Rica international impressed at the World Cup, prompting interest from clubs in a temporary spell, but the Arsenal manager wants to keep him in his squad
The Costa Rica international returned to the Emirates Stadium ahead of the new season following a loan spell at Olympiacos - the latest in a series of temporary moves away from Arsenal.
Campbell has also been loaned out to Lorient and Real Betis in recent years but is expected to challenge for a first-team place at Arsenal this season following a strong World Cup with Costa Rica.
While Campbell is yet to start for Arsenal this season, Wenger maintains the 22-year-old will not leave on loan again ahead of the transfer window closing on Monday.
"We have had a lot of offers for Joel and have turned them all down," Wenger is quoted as saying by The Sunday People.
"There are plenty of clubs - I don't know exactly how many because I said to my assistants, 'He will not go out on loan'.
"If somebody calls them they don't even tell me any more because, when I say no, it's no. But he is definitely a player wanted by many clubs."