The 19-year-old has also been linked with Manchester United.
Bolton's Guillermo Torres (C) in action with Sheffield United's Dominic Calvert Lewin (L) and Ioan Evans
The transfer live ticker from the paper reports (8.05 am) that the Toffees are set to snap up the Blades striker for a fee of £1.5 million.
The Toffees would be beating Manchester United to the signature of the teenager who has been on the radar of Premier League clubs for some time now.
Northampton's Dominic Calvert Lewin celebrates scoring their third goal
Everton have a good record for bringing in players from the lower leagues, as evident with the likes of John Stones and Mason Holgate. The club will no doubt be hoping that Calvert-Lewin would be a similarly brilliant acquisition.
The teenager has been out on loan with the likes of Stalybridge Celtic and Northampton Town in the past and impressed.
However, he is yet to find the back of the net for Sheffield United prior to what appears to be an exciting move to Goodison Park.
He is expected to initially go into the Everton development team as they look toward the future as well as the present.