Widely reported across many media providers, it was said that Everton were interested in taking the Leeds United right-sided utility player on a deal during this transfer window, rather than wait until the summer when the youngster’s contract ended.
In his time at Elland Road, Byram has made 143 appearances and scored on ten occasions.
Toffees boss Roberto Martinez had Byram watched against Ipswich on Tuesday by his chief European scout Ian Atkins and has swooped for the highly-rated 22-year-old.
Everton’s right backs Seamus Coleman, Tyias Browning and Tony Hibbert are all now ruled out with varying fitness issues, meaning John Stones was forced to play out of position in the 0-0 draw with Manchester City on Wednesday.
Others, such as Mason Holgate, Matty Foulds and Luke Garbutt, another with Leeds connections, are being tipped for bright futures at Goodison Park, something Byram is likely to be aware of as he considers his next move.
Leeds have been offered cash plus two unnamed players for Byram by the Hammers.
Byram is a product of Leeds’ youth academy, breaking through to the first-team squad in the 2012/13 season.