Having already offloaded Marouane Chamakh, Arsenal are expected to strengthen their squad this month, with manager Arsene Wenger said to be keen on the Spain international.
Rosell, however, has said the 31-year-old, who signed for Barcelona in a £31m deal from Valencia in 2010, is strictly off-limits.
Speaking to Catalan radio station RAC, he 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."
Other names reportedly on Wenger's hit list include Atletico Madrid frontman Adrian Lopez as well as Argentina midfielder Luca Biglia.
Wenger's men have been left to contend with a busy schedule over the next few weeks, with an FA Cup replay against Swansea as well as a rearranged Boxing Day fixture with West Ham among their regular league matches.
Defender Per Mertesacker feels the Gunners can meet their busy schedule head on.
He said: "We are in a good way but we have to keep our focus on these games [against Manchester City and Chelsea] and the knockout stages of the Champions League. We have to win those games now.
"We are always looking to win something and we can achieve something with this group. We have a lively group so our thoughts are now on the next match, that is the most important thing for us, not what's going to happen in May.
"We have a few targets in our team that are possible this year. We won't talk about it, we'll just see what happens in the next few important weeks on the pitch."