The striker is eager for a move back to the club with which he started his career, making 128 appearances in all competitions during his time at Turf Moor.
Rodriguez has struggled in recent years with injuries, but managed to become a mainstay for the 'Baggies' last season as he made 37 appearances in the Premier League, scoring 7 goals.
Despite his contribution, the team were relegated from the top flight of English football and so the striker is looking for a return to Premier League football.
Sean Dyche's team have had 2 bids rejected for the player so far, and 'Sky Sports' reports that a thrid bid of £18 million will be made.
West Brom have already seen one of their strikers leave the club, as Salomon Rondon joined Newcastle on loan while Dwight Gayle went the other way.