The 33-year-old former midfielder, who recently complained about his lack of first-team action from Jose Mourinho at Inter Milan, is reportedly being targeted by Blues boss Carlo Ancelotti as he looks to bolster his squad ahead of players departing for Africa Cup of Nations duty in January.
Vieira, who spent nine seasons with Arsenal prior to leaving for Inter in 2005, would be a good choice given his vast knowledge of the Premier League. And Drogba says the Frenchman would be welcomed with open arms.
"Patrick Viera will be a good addition to our squad, if we can recruit," he told RTL.
"We know that we will lose two midfielders in January. John Obi Mikel and Michael Essien will be in Angola for African Cup of Nations.
"Vieira? We'd take him anytime. We played against him in pre-season in America. He was ready, in good form and match fit."
The main obstacle to securing a deal for Viera is the Blues are currently unable to make any new signings during the next two transfer windows following the Gael Kakuta saga, but they hope to have the ban lifted following an appeal.
Arsenal last week