"Media and people are free to draw their own conclusions. I have nothing to say on this," Mr Kumar, who is also the JD(U) national president, told reporters after his weekly Lok Samvad programme during which he interacts with public.
Speaking at an event to celebrate 100 years of the Patna University on Saturday, Mr Kumar had sought central university status for it in keeping with public sentiments.
However, responding to the chief minister's plea, PM Modi, who promised Rs 10,000 crore and autonomy to 20 universities - 10 public 10 and private - to enable them to compete globally, said, "I have come here with an invitation to PU and all universities of India to take up the challenge. It is much bigger than what central university status can offer."
This was seen by many as rejection of Mr Kumar's request and media reports suggested that the ties between the two leaders, who came together for the first time after the Bihar chief minister joined hands with the BJP in July, had hit a rough patch.
A tweet by Janata Dal (United) spokesman Pavan Verma over announcement of dates for Gujarat Assembly polls was also seen as an indication of cold vibes between the two parties, which came together after over four years of estrangement.
"The EC must not only be impartial but seen to be so. Why have the dates for Gujarat elections not been announced? We need credible answers," Mr Verma had tweeted this morning.
The tweet placed Mr Verma in the company of opposition parties, which have accused the BJP of pressuring the Election Commission to delay the announcement so that its government could announce sops for the state before the model code of conduct kicks in.
Asked about the Congress's reported plans to elevate Rahul Gandhi as its president, Mr Kumar said, "He is in any case the de facto leader of the party. If we look at the party's history, any other contender for the post seems unlikely. This is an internal matter of that party."
The chief minister, however, took a swipe at the Congress for the continued suspense over Mr Gandhi's elevation, saying "We had heard of this (Rahul becoming Congress president) even when we were together in the Grand Alliance."
When asked whether such a move could boost the Congress's prospects in the 2019 Lok Sabha polls, Mr Kumar said it was too early to say anything but as of now there was no serious challenge to Prime Minister Narendra Modi.
Mr Kumar also dismissed RJD supremo Lalu Prasad's charge that he had decided to break away from the Grand Alliance after his name cropped up in Srijan scam so the Centre saved him.
"They (Lalu and the RJD) should look at themselves and ponder over where they stand today and why. They are only reaping the fruits of what they have sown," MR Kumar said.