Byram is set to be suspended for West Ham’s next two matches, having reached double figures for bookings over the campaign so far.
The right-back has picked up three yellow cards in his first four appearances for the Hammers, after joining from Leeds United in the January transfer window, and Bilic struggles to believe that a player of such slender stature could be so aggressive.
"We are without Sam Byram through suspension; it is hard to imagine a player of his stature getting ten bookings, he is also cup-tied so we will be without him for a few games so we need to find a solution to that," the Croatian boss said.
Byram has actually picked up seven bookings in his last 10 appearances, for both West Ham and Leeds United.
However, it is unlikely to Bilic will be wanting to coach the aggression out of the youngster’s game, as Byram has made such a good start at Upton Park.
The 22-year-old has adapted to playing Premier League football very quickly, and he already looks totally comfortable with playing a regular role in Bilic’s side.
West Ham’s task of replacing Byram has been made harder as both Carl Jenkinson and James Tomkins are out with injury.