Chelsea have confirmed that they have being given permission to speak to the 29-year-old Ukraine striker.
He will undergo a medical later today.
Chelsea will have to fork out a record £38m for the hitman they have being trailing for the past two seasons.
As Shevy moves in Carlo Cudicini couild be moving out.
Chelsea boss Jose Mourinho has revealed he is seeking another goalkeeper.
He is reported as saying: " Hilario is a keeper I am looking at."
The 30-year-old Nacional de Madeira keeper's contract expires in the summer.
"He has the ideal profile in view of our requirements.," added Mourinho.
"I already worked with him and I know he is intelligent. It's necessary to be intelligent in order be a substitute to the best goalkeeper in the world. (Petr Cech)"
Hilario played under Mourinho while they were both at Porto in the 2002/03 season.
Mourinho added: "I need a goalkeeper who is experienced, tranquil, and a team player.
"It is possible that I will find someone with this profile in Portuguese football.
"Hilario is not only bright but he also has common sense."
With Mourinho admitting he needs cover for first choice Petr Cech, it signals the end for the ever-popular Cudicini.