The North Macedonia international is set to continue for at least 2021-22.
The 38 year-old attacker had spoken about retiring after Euro 2020, but appears ready to go around again this new season.
Pandev, capped 122 times by North Macedonia, arrived at Genoa in July 2015.
He has appeared 165 times for the Grifone, contributing 32 goals and 11 assists.
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