Updates from Italy and Germany suggested the Seagulls have made their move for Venezia skipper Michael Svoboda, who has a transfer release clause of almost £5 million.
He is currently involved at the World Cup with Austria but did not feature in their opening match against Jordan.
The 6ft 5in 27-year-old led Venezia to the Serie B title last season.
Albion are facing a busy season of domestic and European commitments and, in terms of central defenders, have released Adam Webster as well as selling Jan Paul van Hecke to Spurs.
Meanwhile Olivier Boscagli and Diego Coppola are likely to attract interest from Europe.
Venezia are also going into a busy summer after bringing in significant new investment as they look to become more than occasional single-season visitors to Serie A.
The one previous piece of business between the two clubs was four years ago when striker Aaron Connolly joined Venezia on loan for the Serie B season.
The deal was cut short midway through the campaign.