Byram, 20, made his first-team breakthough as a right-back last season before being linked with a possible summer move to Manchester City, Newcastle, Everton and West Brom.
But following his return from a long-term hip injury he has started Leeds' last two matches in a wing-back role.
Couzens, who made 29 top-flight appearances for Leeds between 1995 and 1997, said: "When we won the Championship we had Lee Chapman up front, with Mel Sterland at right-back and Tony Dorigo at left-back.
"Ninety per cent of the goals came from crosses being put into the 18-yard box.
"Sam Byram does that now and I liked him playing on the right side of midfield and I thought that could be a new position for him.
"If you go back over the era of how we have scored goals, there has always been a desire to get past people and get crosses in."
Couzens, 38, also thinks big striker Matt Smith, who has scored five goals since arriving from Oldham in the summer, deserves an extended run in Brian McDermott's starting line-up.
"In the team I played in, if the ball went back to Tony Yeboah you knew it wouldn't come back at you and you know you could then make a run, and I think Ross McCormack sees that Smith can hold it up as well," Couzens added.
"Because he's a big lad and held it up against Birmingham, Ross and (Rudy) Austin could make forward runs, which stretched their back four and caused problems, which we haven't had all season so far."