The Leeds boss admits they may need to sell the talent this winter.
The talented Leeds lad is out of contract in the summer and has so far rejected two contract offers from the club this season.
With that in mind the Leeds boss is of the opinion that, if Byram does not sign a new deal in January, he should be moved on.
Evans is quoted by the Yorkshire Evening Post as stating:
"You'd assume clubs would come for Sam in January. There's no real advantage of waiting until the summer. He can't just walk away.
"Sam Byram has to be signing a new contract in January or he goes out of the equation, it's that simple."
Byram would be valued for a compensation package should he leave the club on a Bosman in the summer but it is likely the Yorkshire club could get more money for him in January if they allow a bid to come in for his services.
Byram rejected the first offer of a new deal because of wages and Massimo Cellino publicly criticised him afterwards. The second rejection came after he spent much of the season on the bench and he wanted assurances over first-team football.
After a poor start to the campaign Byram was dropped by Uwe Rosler and then Steve Evans however, on his recall v Wolves last week he scored twice in a 3-2 win.