The former Rayo Vallecano striker has been prolific for the Swans since his arrival in the summer, scoring 13 goals in 18 appearances for the club.
Swansea boss Michael Laudrup now faces a tough battle to keep his prize asset in Wales during the January transfer window.
The Danish manager has put a £30 million price tag on the player's head to ward off interested clubs, but it is thought a more realistic bid of around £10 million would be enough to bring the striker to Anfield.
Liverpool's owners FSG have promised their manager the funds needed to push for a top four position and it looks as if a deal for Michu could happen if Rodgers can sweet talk his former employers.
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