The France international has been the subject of serious interest from Real Madrid and Paris Sain-Germain, with the French champion reported to be leading the chase for him.
However, the Londoners are willing to use the 49 million euros raised by the sale of David Luiz to PSG to part-fund a bid for the former Manchester United man.
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Juventus insist that the club is not willing to sell Pogba and it wants to reach an agreement over a contract extension but the player and his camp do not seem in any hurry.
Pogba's agent, Mino Raiola, is aware that there is likely to be interest in his client this summer which will enhance the team's negotiating position.
The Serie A champion is also aware of the interest in the player from the likes of PSG and, although the priority is to keep hold of the Frenchman, the team could well be tempted into a sale if it was to receive a crazy offer.
Jose Mourinho has made it clear to the Chelsea hierarchy that he wants a marquee central midfielder to partner January signing Nemanja Matic next season.
Pogba has established himself at Juve following his free transfer from United two years ago and was a key player in the club's Serie A triumph this season.
Mourinho is convinced that the France international, 21, will develop into one of the world's finest midfielders and can be a driving force for Chelsea next season.
The Blues have already made discreet inquiries for Pogba and believe that he could be open to a return to the Premier League.
The midfielder has said that he wants to stay in Turin but his agent, Mino Raiola, has spoken of the possibility of him leaving the Italian club.
Chelsea has freed up a place in its squad and on the wage bill after announcing on Friday that the team had agreed to sell Luiz to PSG, subject to a medical and personal terms.
The west Londoners are expected to be active in the transfer market this summer as Mourinho builds a team he thinks can make an even stronger challenge next season for Premier League and Champions League glory.
Chelsea now wants to bring in a dominant player there, capable of scoring goals, with Frank Lampard, who is in talks over a one-year contract extension, expected to feature even less next season should he agree fresh terms.
The team is also considering Tottenham's Paulinho, who is highly regarded by Mourinho despite a mixed first campaign in England following his €20 million switch from Corinthians.