The Clarets were hesitant to meet West Brom's demands for their former striker, but Sean Dyche is losing his patience and is prepared to pay over the odds to get Rodriguez through the door before Thursday.
Sky Sports News understands Burnley will make an improved £18m offer to WBA for striker Jay Rodriguez later today— Sky Sports News (@SkySportsNews) August 7, 2018
The £18m offer will still be short of West Brom's £20m asking price, but it is still a large fee for a Championship player and the Baggies may be tempted to accept.
Bournemouth, Newcastle and West Ham all made enquiries about Rodriguez earlier in the summer but they were put off by West Brom's high valuation, and Rodriguez would prefer a return to the club where he spent the first five years of his senior career.
However, he is a model professional and will not attempt to force his way out of the Hawthorns if Burnley cannot reach an agreement before the window slams shut.
Goalscoring was a problem last season for Burnley, who finished 7th in the Premier League despite scoring fewer goals than 14 of their league rivals.
Rodriguez would go some way to solving their worries in front of goal, and he is proven at Turf Moor, having scored 21 goals in his final season with the Clarets in 2011/12.
An excellent start at Southampton earned him his first and only international cap, but serious injuries have threatened to derail his career ever since.