The 26-year-old is among the Gunners' longest-serving players, having joined from boyhood club Cardiff City in a £5m deal nine years ago.
Wenger believes that Ramsey, who has previous experience of captaining national side Wales, can follow in the steps of Tony Adams, Patrick Vieira and more recently Per Mertesacker in taking on the armband permanently.
"Why not? It is all there. He has maturity, has improved technically and is more conscious of the importance of his technical qualities," Wenger told reporters when asked if Ramsey was captain material. "His game is clean. He has a huge physical power. The target for him will be to have 30 games."