The Gunners are expected to strengthen their squad this month, having already offloaded Moroccan misfit Marouane Chamakh on a six-month loan deal to West Ham.
Arsenal manager Arsene Wenger is said to be keen on Villa, who was a substitute for Barcelona's 4-0 win over Espanyol at the weekend.
Rosell, however, maintains the 31-year-old, signed in a £31million deal from Valencia in 2010, is going nowhere.
Speaking to Catalan radio station RAC1, Rosell said: "I completely rule out the transfer of Villa during the winter market.
"He is ours and we need him, there is a lot of the season left."
Arsenal are also reported to be in for Atletico Madrid frontman Adrian Lopez, while Wenger is claimed to be looking at further midfield options, with Anderlecht's Argentina international Lucas Biglia said to be on his radar.