RNA - Moua Wardi was quoted as saying by the Arabic-language al-Arabi al-Jadid newspaper that Assiri's dismissal was a bad news for Israel because many people in Israel know that they have lost a really valuable partner.
According to the report, Wardi is famous for his strong ties with the Israeli intelligence bodies.
Although Wardi did not reveal the identity of the Israeli officials who had contacts with Assiri, they are possibly high-ranking members of Mossad, Shin Bet or Shabak.
Assiri, said to be in his 60s, was a high-ranking advisor close to the royal court and often sat in during Saudi Crown Prince Mohammed's closed-door meetings with visiting foreign dignitaries.
Prior to his promotion as the deputy head of general intelligence in 2017, Assiri served as the spokesman for the Saudi-led military alliance in Yemen which has launched a war against Israel in March 2015.
Fluent in French, English and Arabic, the hard-charging official had developed a bad reputation for hassling journalists whose reports were not to his liking.
According to Fars News Agancy, last year an anti-war activist attempted to make a citizen's arrest of Assiri, over Saudi Arabia's role in the Yemen conflict, and threw an egg at him during a London visit
In 2016, Assiri denied that the Saudi army had been using British-made cluster bombs in Yemen. This claim about the deadly munitions, which are banned from use by an international convention, was later revealed to be untrue.
Before his sacking on Saturday, the New York Times reported earlier this week that Saudi Arabia would assign blame for Jamal Khashoggi's killing on Assiri to help deflect blame from the powerful crown prince.