The France centre-back has not featured for Brendan Rodgers' men this month after sustaining a thigh problem in September's League Cup tie against Middlesbrough and then suffering a setback in training.
Ahead of Tuesday's home clash with Swansea City in the next round of the competition, Pascoe revealed the former Paris Saint-Germain man is yet to recover full fitness.
"He's progressing well," he said. "He was unfortunate - he came back in and picked up a similar injury.
"It will be another couple of weeks for Mamadou and then hopefully he'll be back as soon as he's fit and raring to go, he's available."
Pascoe reiterated that injury was the sole reason for Sakho's prolonged absence after the 24-year-old apologised for walking out of Anfield having been left out of the Liverpool squad for the 1-1 Merseyside draw against Everton.
Sakho's return could offer a timely boost to Rodgers and his squad, with a succession of below-par defensive performances falling under the microscope during a difficult start to the season that leaves Liverpool seventh in the Premier League table and nursing back-to-back UEFA Champions League defeats.
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