Klopp has one defeat, three draws and three wins in his first seven games in charge, since joining the Reds last month, with the undoubted highlight coming in a 3-1 win away to Chelsea on October 31.
The charismatic former Borussia Dortmund coach was keen to profess that he needed time to get his new squad to adjust to his ideas upon his arrival at Anfield, although there have been signs that the ex-BVB boss is getting his methods across.
The famous 'geggenpressing' style that Klopp used to maximum impact at Dortmund has been evident at Anfield already, with the likes of Mamadou Sakho, Philippe Coutinho and, perhaps most notably, Adam Lallana all showing signs of improvement under the German.
Speaking to the Liverpool Echo about Klopp's first month in charge, former midfielder Molby feels that the Liverpool manager is no mircale worker, and the Dane called for him to be backed in the January transfer window to add to a squad that has designs on securing a place in the top four this season.
Molby wrote: "A month into his Anfield reign I think that Jurgen Klopp has done a good job. I would give him a seven out of 10 so far. I think that we now look like a team that could win more games and perhaps go on a run of wins.
"But there is a limit to how far you can take any football team and Jurgen Klopp is a football manager, not a magician. He will want to move forward with a group of players, some of whom are already at Anfield and some of whom are not here yet.
"I would like him to do business in the January window because there is everything to play for. For Klopp as a new manager he will instantly have identified something he can improve upon – he will be thinking 'we're missing this and I know where to go to get it'.
"For me there is nothing wrong if he wants to go back to Germany, Jurgen should work in the market he knows best."
Klopp's side return to action on November 21 when they travel to league leaders Manchester City, and the Reds will still be without Jordan Henderson and Daniel Sturridge, while Mamadou Sakho misses out having picked up a knee injury in the 2-1 defeat to Crystal Palace before the international break.