Liverpool's transfer business under Brendan Rodgers was largely poor.
Klopp has stressed that he has control over Liverpool's transfers, but Nicholas predicts that he will test the Reds' board in January.
The former Scotland international player says that Klopp will demand a specific target which he wants brought to Anfield, to make sure that the owners are true to their word.
"It's alright him saying in press conference this week that he has the first say and the last say [on transfers]. Boards and owners may tell him that, but they don't always stick to that conclusion," Nicholas said. "They think 'well, I'll drag him along for the first few months'.
"He wanted to come to Liverpool, and he wants to solve the issues, but there is a lot to be solved. I think he'll go an identify someone in January, and he'll make sure they're someone of significance. He'll say 'I want him, and you must get him for me'.
"Then, if the guys don't get him. What happens? Does he demand even more out of them? Liverpool must support him wholeheartedly."
Klopp's arrival at Anfield has created great excitement for the future, with many Reds supporters believing he can get them challenging for the Premier League title.
The German boss's first match ended in a 0-0 draw with Tottenham Hotspur, but improvements were already on display.
Liverpool ran further than they have in any other match this season, while they seemed much more secure defensively than they have in previous weeks.
Although there is still much for Klopp to work on, it was a heartening display, and he will be hoping that his side can continue to progress over the coming weeks, as they chase a top-four place.