The Baggies have been looking to strengthen their attacking options in recent weeks and it is understood Vydra would fit the bill.
The 21-year-old spent the entirety of the last campaign out on loan with Championship side Watford, where he excelled with 20 goals as the Hornets narrowly missed out on promotion.
He has struggled for first-team opportunities with Udinese since moving from Banik Ostrava in 2010 and West Brom will now be hoping to persuade the Italian club to allow the Czech to move to the Hawthorns for one season.
While boss Steve Clarke has bolstered his forward line with the acquisition of Nicolas Anelka, with the Frenchman starting his career at the Midlands club in impressive fashion after notching seven goals in as many pre-season games, he will be without the services of Romelu Lukaku, who returned to parent club Chelsea over the summer after leading the line for West Brom last season.
The Baggies had been linked with former Chelsea frontman Salomon Kalou, now with Lille, but it is understood they are now fully focused on securing Vydra's services.
They may have to move quickly, however, as the Czech Republic international has also been mentioned as targets for Premier League rivals Sunderland and West Ham during this transfer window.