Sitting in 15th position in the Premier League with just 12 goals from 14 matches, the Gunners are expected to make at least one attacking addition at the start of 2021.
According to The Mirror, the North London outfit have taken an interest in Gomez, who is expected to be available for a cut-price fee.
Valencia's financial problems are likely to lead to sales being made over the coming weeks, regardless of any player's status at the Mestalla.
Gomez, one of the Spanish side's most prized assets, scored his fourth goal of the season on Saturday as Los Che earned a 2-2 draw at Barcelona.
However, despite possessing a £125m release clause, the Uruguay international is expected to be available for a fraction of that price tag next month.