The 21-year-old, who scored 20 league goals while on loan at Watford last season, had been expected to return to the Hornets next season.
However, according to his representative Ondrej Chovanec, Vydra has set his sights on a move to the Premier League.
"We agreed that none of the offers (for a permanent transfer) are in the region that would interest Udinese," Chovanec told isport.blesk.cz.
"They don't want to sell him for £8million, so they have given us freedom to discuss loan spells with the Premier League clubs that are interested.
"At the moment we have offers from four Premier League clubs - West Brom, West Ham, Swansea and Sunderland."
A number of Italian clubs are also believed to be monitoring proceedings.