Klopp has reverted to a back four, as opposed to a back three often favoured by Brendan Rodgers, which saw both Nathaniel Clyne and Alberto Moreno operate as wing-backs.
In his Liverpool Echo column, Molby seems to indicate that he feels Klopp has more faith in Moreno than Rodgers did.
He said: "What's interesting for the Spaniard is that, rather than being told to work on his weaknesses as Brendan Rodgers wanted, he has instead been given the opportunity to show off his strengths by Klopp.
"Instead of being asked to do things he can't, Moreno is doing the things he can.
"I'd heard rumours Rodgers thought the Spaniard wasn't tall enough for a full-back and wasn't a good enough defender."
Moreno does seem to have thrived somewhat under Klopp. Though there are areas of his game that the Spaniard needs to work on, such as his final ball going forward and his tendency to switch off at the back, his ability to be aggressive and get up and down the flank relatively easily has been used by Klopp to pretty useful effect.
Nathaniel Clyne joined the Reds in the summer for £12.5 million, as reported by the BBC, and seemed to have got off to a pretty good start, but struggled with the change of system. Now he is back in a preferred full-back role, he seems a little more at home.
Molby thinks Clyne has impressed over the past six games, saying: "Clyne may catch the eye with his runs down the right flank, but more important is that he is a full-back who clearly enjoys defending.
"He knows his defensive role, and knows the right time to get forward."
Certainly, the pair look more suited to their defensive duties than they did before Klopp's appointment in October.
Clyne arrived at Liverpool with a reputation as being one of the best right-backs in the league. Recently he has been quietly impressive - including getting his first goal in a League Cup tie while playing on the left flank - but has shown he can provide that natural width and final delivery going forward while putting in solid defensive displays.