Two other people familiar with the case corroborated the details.
A third person said Kovrig was being confined to a single room, but despite the stress remains lucid.
The comments were made in recent days. All the sources requested anonymity citing the sensitivity of the situation.
China's Foreign Ministry did not immediately respond to a request for comment. It has said that the lawful rights of both men were being fully protected.
China's Ministry of State Security, which is leading the investigation into Kovrig, has no publicly available contact details.
"Our previous comments on this case stand," said Adam Austen, a spokesman for Canadian Foreign Minister Chrystia Freeland.
The Canadian government has said several times it saw no explicit link between the arrest of Meng, the daughter of Huawei's founder, and the detentions of Kovrig and Spavor.
But Beijing-based Western diplomats and former Canadian diplomats have said they believed the detentions were a "tit-for-tat" reprisal by China.
A Canadian court last week granted Meng bail. If a Canadian judge rules the case against Meng is strong enough, Canada's justice minister must next decide whether to extradite her to the United States. If so, Meng would face U.S. charges of conspiracy to defraud multiple financial institutions.
China on Thursday said a third, female Canadian is undergoing "administrative punishment" for working illegally, after Canada's government confirmed the detention.