Prof Ratemo Michieka of the Inter-Public Universities Councils Forum on Tuesday said the lecturers had a counter-offer from the government.
However, he declined to disclose the contents of the counter-offer.
The government has given striking lecturers an offer, signalling hopes for an end to the three-week work boycott in public universities.
“We are waiting for their feedback once they are done with analysing the proposal, which is very good,” said Prof Michieka.
The lecturers are set to meet with the forum on Wednesday for talks that many hope will lead to an agreement.
On Tuesday, non- teaching staff held talks with the universities’ management and another meeting is scheduled for Thursday.
“We will only talk of calling off the strike once we have seen this offer that the government is talking about,” said Multimedia University Universities Academic Staff Union (Uasu) chapter secretary-general Onesmus Mutio.
Uasu chairman Muga K’Olale declined to discuss the offer with the media.