The Mirror reports that Pulis is ready to make a £4million bid for the Brazil international.
Lucas came close to joining Stoke in the summer, but Liverpool boss Roy Hodgson wanted to keep the midfielder at the club.
Hodgson could be prepared to sell Lucas in the January transfer window in order to raise funds.
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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.