Tottenham star Kane is among six nominees for the prestigious individual award this season.
Fulham winger Ryan Sessegnon and Manchester City goalkeeper Ederson are among the other nominees.
West Ham right-back Byram, who joined the London club from Leeds United in January 2016 for a transfer fee reported by The Independent to be worth £3.7 million, has revealed that he voted for Spurs striker Kane for the PFA Young Player of the Year award.
Kane is one of the best players in the Premier League, and the 24-year-old striker could win the PFA Young Player of the Year award.
The England international has scored 25 goals in the league so far this season and could win the Premier League Golden Boot as well.
Tottenham look set to finish in the top four of the Premier League this season yet again.