Pogba has been linked with a move to Stamford Bridge in recent seasons and the arrival of former Juventus boss Antonio Conte has reignited their interest.
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The France international's agent Mino Raiola said last week a deal looked unlikely, although he wasn't prepared to completely rule out a move.
And the 23-year-old has reportedly set his sights on winning the Champions League with Juve this term after losing last year's final to Barca.
Pogba has been in fine form this season, making 50 appearances for club and country, scoring 10 goals and will represent France at this summer's European Championships.