Higgs has watched most of the season from the sidelines due to a thigh injury and left-back Parker has been out since the opening day, first with a troublesome groin and more recently a knee problem.
Both players came through a midweek reserve-team outing unscathed and might make the substitutes' bench at Elland Road.
Striker Tresor Kandol could also return to the matchday squad, while winger Max Gradel staked his case for a bigger role with a hat-trick in the second string's 5-0 win over Lincoln.
Manager Simon Grayson, who has no new injury or suspension worries, must decide whether to stick with young defender Aidan White or opt for the more experienced Leigh Bromby in his starting line-up.
Gary McSheffrey and Neil Kilkenny are vying for one of four midfield places and veteran striker Paul Dickov is waiting for his first start as Leeds look to consolidate in second place by bouncing back from last week's defeat at Southampton.