The Welsh side are back in the EFL after a lengthy absence and are determined to make a splash in League Two.
They are looking for experience to help them on their way and have zeroed in on 34-year-old winger McClean.
It is claimed that Wrexham are set to pay in the region of £250,000 to take McClean to the Racecourse Ground.
Snapping up the Ireland international will be seen as a big statement of intent on the part of Wrexham, with the new season having now arrived.
McClean has played the majority of his football in either the Premier League or the Championship and has not played below League One level.
Wrexham will be looking to quickly get the deal over the line and place him at the disposal of Phil Parkinson.
The Welsh side start their League Two push on Saturday by playing host to MK Dons.
