The 24-year-old has been a key player for the Dutch giants this season, making 17 Eredivisie appearances as well as featuring 10 times in the Europa Conference League.
However, Senesi has just under 18 months remaining on his contract and is considering his options ahead of a proposed move to one of Europe's top five leagues.
According to Football Insider, both Brighton and Newcastle are weighing up January moves to sign the Argentine, who could be available this month for around £16.8m.
The Magpies are believed to have identified Senesi as an alternative to their top defensive target Sven Botman, who is unlikely to make to switch to St James Park from Lille in January.
The Seagulls are also having to cope without club captain Lewis Dunk, who could be ruled out until March with a knee ligament injury.