The Reds have been in the market for a right-back all summer to offer competition to Tendayi Darikwa.
Forest boss Aitor Karanka has been keen on adding Byram to his squad and confirmed his interest yesterday.
And a Hammers insider on Twitter has offered fans an update on one of the window’s drawn out transfers.
“Forest offered a loan, we want to sell! Last I heard we were trying to come to an agreement where by the loan fee is higher and the final purchase is therefore lower and I think talks are still on going,” posted @ExWHUemployee.
Byram, formerly of Leeds United, would become Forest’s 12th signing of the summer transfer window.
The Reds face West Brom at The City Ground tonight (Tuesday 7th August), with Darikwa likely to start once more.