The Clarets have made signing a striker a priority after unexpectedly losing Chris Wood to relegation rivals Newcastle United earlier this month.
They have been linked with a number of options, but it is Dutch hitman Weghorst who is being lined up as a deadline day signing for the club.
Weghorst, 29, is expected to be put through his medical paces by Burnley on transfer deadline day morning, before then signing a contract to join the club.
The striker is currently on the books at Bundesliga outfit Wolfsburg.
He scored 20 goals in 34 Bundesliga games for Wolfsburg last season and this term has struck on six occasions in 18 league matches.
Burnley will be hoping that the former AZ Alkmaar man can quickly hit the ground running in the Premier League.
The Clarets have struggled to score goals this season, managing just 16 in their 18 Premier League games so far.
