The 28-year-old has been a catalyst in each of the team's last two victories, scoring the opening goal at Wigan Athletic and a crucial equaliser against Tottenham Hotspur.
Molby has been highly impressed by the wide-man's form and believes Brendan Rodgers deserves credit for the way he has handled the player.
"It's unusual for a manager to be as blunt as Brendan Rodgers was with Stewart Downing - but telling the winger he could leave in January certainly did the trick," Molby told the Liverpool Echo.
"Rodgers got the reaction he was hoping for, with Downing having since become a reliable member of his Liverpool squad.
"Downing continued to impress in last weekend's win over Tottenham. He's playing ever so well - he looks full of running and has got his confidence back.
"It was such an important goal he scored to make it 2-2 as that galvanised Liverpool. I know the 'keeper made a hash of it but that wasn't an easy chance.
"Downing was expected to score but what I liked was the way he kept his composure to score with his weaker foot.
"Realising how close he was to leaving Liverpool has transformed Downing. He will have looked at it before Christmas and thought 'who is going to come in for me?' He will have worked out his best bet was to knuckle down and prove the manager wrong.
"We knew when we bought him he had great ability from his performances for Aston Villa but it's only now we're really seeing it.
"I think he's already shown enough in recent months to have convinced Rodgers he should be part of his plans beyond this season."