The 25-year-old Spaniard has been in fine form for the Toon this season and is seen as an ideal replacement for the outgoing Paul Konchesky.
Liverpool manager Kenny Dalglish sent Konchesky on loan in the January transfer window after the summer signing struggled for form at Anfield.
He has instead preferred to play an out-of-poisition Glen Johnson at left back for the rest of the season until they can bring in a long-term replacement.
Enrique has been linked with Liverpool before but fresh reports have surfaced after Anfield Director of Football Strategy Damien Comolli was spotted at Ewood Park this weekend watching Enrique and Newcastle take on Blackburn Rovers.
The highly rated defender is regarded as one of the best players in his specialist position and Magpies fans will be desperate to keep hold of the Spanish star, particularly after having already lost former Toon legend Andy Carroll to Liverpool in the January window.
Enrique was brought to St James’ Park by former manager Sam Allardyce in August 2007 from Villareal for a fee believed to be around £6m, but since his rise to prominence, Newcastle chief Mike Ashley is thought to want at least double that if the player is to be sold.
New Liverpool owners NESV have already shattered the clubs record transfer fee since taking over when they signed Carroll from Newcastle for £35m, proving their financial commitment to the cause as they look to restore the Anfield club to its former glories.
Additional interest from Manchester United could be the only stumbling block as Sir Alex Ferguson continues to look for a replacement for Red Devils star Patrice Evra who is rumoured to be unhappy with life at Old Trafford and has been continuously linked with a move away from Manchester.
A summer transfer tussle between Manchester United and Liverpool will only play into the hands of Newcastle as they look to gain the maximum possible fee for one of their remaining leading stars.