On 21 January 2020, Russian Premier League club PFC Sochi announced that Kokorin will join them on loan until the end of the 2019–20 season. He initially refused to report and was moved to Zenit-2. He eventually agreed to the loan and it was confirmed by Zenit on 17 February 2020.
On 19 June 2020, Kokorin scored a hat-trick in the first match back following the suspension of the Premier League due to COVID-19 pandemic. The match was a notable 10–1 victory over FC Rostov. Rostov were forced to play their youth side though after their senior and reserve sides, 43 players in total, were forced to quarantine.
On 2 August 2020, Spartak Moscow announced the signing of Kokorin to a three-year contract, with the option of an additional year, after his Zenit St.Petersburg contract had expired.