Sources said the two discussed the issue during their meeting and a solution to resolve the issue of setting up the varsity can be expected soon.
The Centre has proposed to set up the varsity at Gaya, but the state is seeking to open it at Motihari.
Sibal had said in the Rajya Sabha last week that he was "willing" to sit down with Kumar and discuss the issue.
"I have rung up Nitish Kumarji, I have requested him for an appointment, I am willing to sit with him and decide as to what we should do about the Bihar Central University as well. We have no problems," Sibal had said.
"Let us sit together, and let us see how this can be done," Sibal said.
Earlier, more than a dozen MPs of Bihar, mostly belonging to JD-U and BJP, staged a protest rally here demanding that the varsity be set up at Motihari as Bihar Assembly had also passed a unanimous resolution in this regard.
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The varsity proposal has created a rift between the Bihar chief miniser and Sibal, who has favoured Gaya as an ideal location for the institution as the place is close to an international airport and is well connected.
"When the state legislative assembly has unanimously passed a resolution for setting up the university in Motihari, I fail to understand why Sibalji is against it," BJP MP Radha Mohan Singh had said here last week.
Sibal has insisted that Gaya as a location will help the varsity get quality faculty and also help it develop as a centre of excellence. The Ministry has been allocated land by the Defence Ministry there for the varsity, which at present is functioning from a temporary accommodation in Patna.