The defensive duo, who have been in disappointing form this season, have found themselves on the bench for the past two Gunners games, with Laurent Koscielny and Lukasz Fabianski preferred in the starting lineup.
This has cast doubt over the futures of the pair at the Emirates Stadium, but Wenger denies that he might be about to lose both players.
"Szczesny? I rate him highly and have a big respect for what he's done," Wenger told London 24.
"And Vermaelen? He is a very important part of our squad. He has a fantastic attitude and motivation."
Szczesny and Vermaelen were both unused substitutes during Arsenal's 2-0 win at Swansea City on Saturday.