The Brazil international has found himself on the fringes of the Arsenal first-team this season, and was widely criticised for swapping shirts with former-Gunners captain Robin Van Persie when Arsenal played Manchester United earlier this season.
The report claims Wenger is ready to listen to offers for Santos when the transfer window reopens, but the left-back insists he wants to stay in north London.
The Daily Mirror carries Brazilian reports in which Santos said: "I received calls from interested clubs in Brazil, Turkey and Italy, but it is just speculation. Nobody handed me anything.
"The coach, who is also a manager, never said anything to me. I know he is very transparent and I am focused on staying at Arsenal, winning a title, doing well in the Champions League, and I have three more years of my contract. I'm happy here."
The 29-year-old joined the Gunners from Fenerbahce in a £6m deal last year, but the Brazilian has struggled to cement a place in the first-team, despite injury to his main competition Kieran Gibbs.
Santos himself has spent time on the treatment table, but the fullback is keen to stake his claim for a regular spot in the Arsenal side now he's back to full fitness.
The Daily Mirror claims clubs in Turkey and Brazil are interested in Santos, including his former-club Corinthians, but the left-back is thought to enjoy his life in London.