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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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
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