The fee is more than double their current club record of ??3.2m, which they paid West Brom to sign Nathan Ellington eight years ago.
The Championship runners-up, preparing for their first season back in the Premier League after an eight year absence, are battling with West Ham United, Inter Milan and Valencia for the Argentina international’s signature.
Perotti only moved to Genoa from Sevilla for ??250,000 last summer; Sky sources understand Sevilla will be due 20% of any transfer fee.
Perotti, who began his career at Boca Juniors before breaking into the senior ranks with Deportivo Moron, has two caps for Argentina, making his international debut when he moved to Sevilla in 2009.
He would become Watford’s second signing of the summer after the Championship runners-up confirmed the signing of Austria defender Sebastian Prodl from Werder Bremen.