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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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.