Chelsea have had two bids rejected but could go back in with another this week.
Pogba, meanwhile, looked set to stay at Juventus for another season after failing to agree a move to Barcelona.
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Paul Pogba is back on Chelsea's radar
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Manchester City were also keen but have since settled for Fabian Delph and are chasing Kevin De Bruyne.
A move for Pogba would set the Blues back in excess of £60million after the France midfielder's stunning rise since leaving Manchester United in 2012.
He helped Juve to the Champions League final last season, has won three Serie A titles and was voted young player of the tournament at last summer's World Cup in Brazil.