The experienced striker has caught the attention of the Gunners in recent weeks, but his current club insist they are keen to hold on to him until the end of the season
Goal.com revealed earlier this month that Arsenal have made a formal approach for the Spain international as they aim to strengthen their attack this winter.
The Gunners have also tabled a £10 million bid for Atletico Madrid striker Adrian, but are believed to have identified Villa as their preferred back-up choice should no deal materialise for the 24-year-old.
However, the Catalans have stressed that Villa still has a role to play at the Camp Nou side as they are fighting for silverware in La Liga, Copa del Rey and the Champions League.
"I absolutely reject the notion that David Villa could leave Barcelona this winter," Rosell was quoted as saying by Sport.
"David is one of our players and we need him in the second half of the season."
The 31-year-old has a contract with Barcelona until the summer of 2014.