The Sun reports that Mourinho wants to offer Chelsea a sensation swap deal that would see Lampard move to the Bernabeu.
Mourinho is ready to exchange former Spanish Under-21 international Esteban Granero for the England star.
Granero is valued at £6million and has recently been linked with the likes of Arsenal and Liverpool.
Lampard has had a torrid time under new Chelsea coach Andre Villas-Boas at Stamford Bridge.