Pogba signed a new contract earlier this season, committing himself to the Italian champions until 2019, but his agent, Mino Raiola, revealed in January that his client will not see the deal through, claiming that the 21-year-old will move on inside the next 18 months.
Chelsea and Madrid are believed to lead the race to sign a player who could fetch a fee of over €100 million and Anelka, who has played for all three clubs involved in this particular transfer saga, feels that his compatriot would be best served by a switch to Stamford Bridge.
"My preference is Chelsea, who have really big players and [owner Roman] Abramovich's financial power, or Real Madrid, who are one of the biggest clubs in the world - if not the biggest," the 35-year-old told France Football.
"And I can see him doing well there, with regards to his playing style and the coach there. Carlo Ancelotti would get a lot out of him.
"In his head, Paul will already know clubs that he wants to play for."
Anelka lifted the Champions League with Madrid at the end of his one and only season in Spain, in 2000, and claimed an English title and two FA Cups over the course of his four-year stay at Chelsea between 2008 and 2012.