The Barclays Premier League side is believed to have made a two million euro bid for the 26-year-old who scored 15 La Liga goals last season.
According to Marca.com, the Spaniard was given the all clear to discuss personal terms with the Welsh side on Monday.
Michu has a four million euro release clause from his contract but the Madrid-based side has been struggling financially, with players threatening to leave last season in a row over unpaid wages.
La Liga side Sevilla were also believed to be interested in signing Michu and according to Rayoherald.com, could allow the midfielder to stay at Rayo on loan next season.
New Swansea manager Michael Laudrup said he thought the Spanish transfer market offered good value for money when he joined the Welsh side following the departure of Brendan Rodgers.
The move means Michu could be set to fill the place left by loan star Gylfi Sigurdsson who left the Liberty Stadium to join Tottenham.