The USA international is believed to be among the players Chelsea are looking to ship out of the club at the end of the season.
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Pulisic's contract is up at the end of next season and the Blues are likely to be keen to recoup a fee for the 24-year-old.
Having made just eight league starts this season, Pulisic is desperate for more game time but faces stiff competition after Chelsea's huge recruitment drive.
The additions of Raheem Sterling, Mykhailo Mudryk, Noni Madueke and with Christopher Nkunku set to arrive this summer has left Pulisic in limbo surrounding his future.
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But recently crowned Serie A champions, Napoli, are set to offer the American a route out of west London, the Daily Mail reports. The report also says Juve have expressed an interest in Pulisic.
Any potential deal could see Napoli's star striker, Victor Osimhen, discussed as Chelsea step up their search for a striker.
However, Napoli have made clear their intention to keep hold of the Nigerian this summer despite interest from Chelsea and Manchester United.
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A figure of around £130million has been sounded out for Osimhen but Chelsea may need to sell before they can splash that kind of fee, due to Financial Fair Play regulations.
One avenue Chelsea may explore is of striker Romelu Lukaku who is currently on loan at Inter Milan.
The Belgian has made clear his desire to remain with the Nerazzurri beyond the current season and Chelsea may look to cash in on the £97.5m signing.
Mauricio Pochettino looks set to take over at Stamford Bridge next season with a deal expected to be concluded imminently.