Lukaku could make his debut for Manchester United in the early hours of Sunday morning when they take on LA Galaxy in their first match of pre-season.
The Belgian joined United for Everton in a deal worth around £75million on Monday having looked set to join Chelsea.
Blues boss Antonio Conte told Diego Costa that he was no longer wanted at Stamford Bridge and made Lukaku his top transfer target.
And Conte is understood to be angered at losing out on the 24-year-old striker to United.
Romelu Lukaku is set to make his pre-season debut for Manchester United overnight
You think maybe Jose was stopping Lukaku going to Chelsea to make them stronger as he is probably the best target man around
Chelsea now face having to find a new striker to replace Costa with Alvaro Morata and Pierre-Emerick Aubameyang linked.
Neville admits Lukaku's move caught him by surprise but feels it may have been a calculated decision by Mourinho.
"It caught me by surprise, I thought they were going to go for Morata and Jose said they actually bid for Morata," he said to talkSPORT.
"What Jose likes in all the teams he has managed is a target man and if Diego Costa leaves Chelsea you think maybe Jose was stopping Lukaku going to Chelsea to make them stronger as he is probably the best target man around."
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