The Costa Rica international joined Arsenal in 2011, but he has yet to make a first-team appearance for Arsene Wenger’s side due to work permit issues.
He has spent time with Lorient, Real Betis and Olympiakos, and has been linked with another loan move away from the Emirates Stadium.
AC Milan have already acknowledged an interest in the 22-year-old, while Galatasaray have also been linked with an approach for Campbell.
However, after impressing for Costa Rica at the World Cup in Brazil, Campbell is keen to be given an opportunity at Arsenal.
“The Premier League’s the most interesting in the world and I’ve always wanted to play here. It’s my dream. And I believe I’m good enough,” Campbell told The Sun.
“I’ve played around 100 games in three different divisions in Europe. Lorient in France, Real Betis in Spain and Olympiakos in Greece, where I played Champions League too.
“I’m confident of being successful in any division in the world.”