The Seagulls are keen to add to their front line this summer as they look to extend their stay in the top flight beyond a single season.
The striker scored the winning goal for Portugal during their Euro 2016 success but his current employers are believed to be ready to listen to offers for him this summer.
English publication 'The Daily Mail' reports that Harry Redknapp's Birmingham City have also asked after the 29-year-old's availability but it is believed that they would struggle to compete with interest from the Premier League.
The Portuguese striker scored six goals in 31 Ligue 1 appearances last season.