Spurs will have to meet the midfielder's £26million release clause to pry him away from old boss Jose Mourinho.
There are also doubts over Harry Winks' Spurs future.
And Pellegrini, 25, is seen as the ideal man to fill their shoes if they leave.
However, cash-strapped Tottenham will have to come up with £26m to trigger Pellegrini's Roma release clause as he is one of their key players.
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