Arsenal and Tottenham both offered the Inter Milan midfielder a return to north London in the summer before the France international opted to stay at the San Siro.
Time to go: Vieira (left) could feel he need to try his luck away from Inter
But Vieira is well down the pecking order under former Chelsea boss Jose Mourinho and the 33-year-old, who watched the Blues beat Liverpool on Sunday, will consider a move in order to play first-team football ahead of the World Cup.
Chelsea have been banned from signing any players during the next two transfer windows and will lose John Mikel Obi and Michael Essien from their midfield during the Africa Cup of Nations.
The club has appealed against their suspension and Drogba wants his manager to move for ex-Arsenal skipper Vieira if it is upheld.
Plenty to say: Drogba has told Chelsea boss Ancelotti to swoop for Vieira
He told The Sun: 'It would be a good move for Chelsea to bring Patrick in. Don't forget we are going to miss several players in January, particularly in midfield, because of the African Nations Cup.
'We played against Vieira last summer and he was very strong.'
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