The Czech Republic striker scored 20 goals in 27 Championship starts while on loan at Watford for the whole of last season.
And Albion have made a bid to bring him back to England on similar terms.
Vydra's goals helped Watford to the Championship play-off final last season and earned him the Championship Player of the Year title at the Football League Awards.
Gianfranco Zola said last month he had not given up hope of re-signing Vydra, but the 21-year-old has been linked with several Premier League clubs and Albion are the first to show their hand.
Steve Clarke has already brought in one striker this summer in Nicolas Anelka, but Romelu Lukaku is back at Chelsea following the end of his loan spell and Peter Odemwingie is a target for Al Nasr of Dubai.
Vydra would be keen to play in the Premier League during the coming campaign following his impressive last season at Vicarage Road.
Asked if he would like to be on his way to the English top flight before the transfer window closes, Vydra told isport.blesk.cz: "It would be my dream. I would like to play in that competition.
"I have not been thinking about specific clubs because there has not been anything. After the international friendly (on 14th August) I would like to move on finally."
Vydra admits a move this late in the window would be far from ideal, but he is reluctant to remain in Italy where he finds himself some way down the attacking pecking order.
He added: "I know it's not ideal because the leagues are starting this week or the next weekend. I would come in as a new player without having spent pre-season preparation with the team and that would make my position more difficult at the beginning.
"If someone does sign me, hopefully they would want me to play.
"Training here has been the same as it would have been somewhere else. In the next few days it should be resolved."