Reds boss Brendan Rodgers is thought to be keen to reinforce his attacking options next month, with his team becoming overly reliant on Uruguayan striker Luis Suarez.
Michu has been in fine form since his summer arrival at the Liberty Stadium, weighing in with a staggering 13 goals in all competitions so far.
The Swans’ manager, Michael Laudrup, has placed a £30m price tag on the Spaniard’s head to keep interest at bay, but it’s thought that the Anfield club will offer £10m, five times the fee the parted with for his signature, next month.
Michu is, by trade, an attacking midfielder, but has been impressive playing as a central striker in recent weeks.
Rodgers sees the 26-year-old as an ideal fit for his current system with his sound technical ability and passing range impressive so far this season.
Liverpool are also thought to be chasing Chelsea’s back-up striker Daniel Sturridge, however his £80,000-per-week wage demands could scupper any deal.
Theo Walcott and Tom Ince are other options, but it’s unclear as to whether the club will push through moves during January.