The 23-year-old is expected to receive plenty of interest at the end of the season after the Black Cats were relegated to the Championship.
Pickford has been a consistent positive in an otherwise dreary campaign for Sunderland, and he showed his ability once more by preventing a drubbing at the hands of Arsenal, who eventually earned a 2-0 victory on Tuesday night.
"Pickford had an exceptional night," Wenger told reporters. "I think we had 36 shots at goal, the highest in the Premier League. The keeper saved 11 of them, so he did extremely well, but we have plenty of goalkeepers.
"We have Petr Cech, Ospina, we have Wojciech Szczesny who is only on loan at Roma and has had an exceptional season. We [also] have Damian Martinez. If there is one thing we do not need to buy, it is a goalkeeper."
Pickford has been at Sunderland for his entire career.