The Clarets were hoping that the Baggies would have accepted a reduced price for the duo following the Midlands’ side’s relegation to the Championship last season.
European Challenge requires more defensive depth to succeed
Burnley manager Sean Dyche has pinpointed quality in depth as the area to improve the most following last season, in which the Clarets regularly named an unchanged or rarely changed side.
With a European adventure to plan for this summer as well as maintaining a high league position, central defence was a place the club definitely needed to address after getting by with only three recognised players in that position, Ben Mee, James Tarkowski and Kevin Long.
Tarkowski and Mee have been linked with moves away to top six clubs after stunning performances that helped the Clarets to one of the best defensive records in the Premier League.
28-year-old Dawson made 28 appearances in the Premier League last season and has been with West Brom since 2010, making 153 appearances in the top division for the club.
The big centre half would bring added impetus to the Clarets in the both boxes and can play in a central two or in a three at the back formation, with Sky Sports believing that his current club value him at about £12 million on his own.
Losses going forward shouldn’t be forgotten either
Depth going forward will also to be improved after the Clarets lost Scott Arfield to Rangers at the end of last season and Georges-Kevin Nkoudou returned to Tottenham Hotspur after his loan deal left a lot to be desired.
Jonathan Walters also looks set to be on his way so Dyche will be looking to get some replacements in going forward before the start of the Europa League campaign.
Rodriguez started his career with the Clarets where he made 105 appearances, scoring 31 times before moving to Southampton where he made 104 appearances, hitting the net 26 times.
Rodriguez then made the move to the Baggies in the 2017-2018 season where he scored seven times in 37 games.
West Brom have valued Rodriguez at £20 million after paying £12 million for the striker in the summer of 2017.
West Brom could be holding out for an offer in the region of £30 million, but some reports suggest that the Baggies could have a £40 million asking price for the duo.
Burnley finished the Premier League season in seventh, qualifying them for the Europa League, whereas West Brom were relegated to the Championship despite a late surge in form.