Jones died following an accident on the £500m Laing O’Rourke job on Monday.
The 26-year-old Everton fan suffered severe head injuries and was declared dead after being taken to Aintree Hospital.
Everton said: “The loss of Michael Jones, a lifelong Evertonian who followed the Blues home and away, has left us all devastated.
“The thoughts of everyone at Everton remain with Michael’s family, friends and colleagues.
“We will now be working with Michael’s family on an appropriate and lasting tribute. Michael Jones, forever in our hearts.”
Laing O’Rourke has suspended work at the project while HSE and Merseyside Police carry out investigations.
A post-mortem to establish the cause of death is due to take place today.