Portuguese newspaper A Bola claims the arrival of Guarin will facilitate the departure of Essien, who has been at Chelsea since his €30m move from Lyon in the summer of 2005.
Mourinho and Essien have a close working relationship, the Ghanaian followed the Chelsea boss to Real Madrid on loan last season and often refers to him as his "second father".
But Mourinho will have a surplus of midfielders should he complete the signing of Colombian international Guarin.
The Inter Milan star has been heavily linked with the Stamford Bridge club in recent weeks, with reports suggesting a £15m fee has been agreed between the two clubs.
The 27-year-old would join Frank Lampard, Ramires, John Obi Mikel and the injured Marco van Ginkel at Stamford Bridge.
And the report claims Mourinho would be happy to allow the 31-year-old Essien look for a new team in the January transfer window.