The 23-year-old wideman has graduated through the ranks at the Nou Camp after joining the Catalan giants in 2004, but after making the breakthrough into the first team last season he has struggled to feature this season.
His four La Liga appearances this term have all come as a substitute and Dalglish, who looks set to be offered the Anfield hot-seat on a permanent basis, is hoping to lure the Venezuela-born star to Anfield.
Jeffren, who has played at right-back in his time with Barca, is contracted until 2012 and will cost around £8.7million due to the buy-out clause in his contract, but that won’t put off Dalglish.
The former Spain under-21 star, who netted in the 5-0 win over Real Madrid earlier in the season, is the type of speedy, skilful forward the Scottish boss is trying to add to his squad.
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Kenny Dalglish Chasing Barca’s Jeffren