The Clarets have successfully returned to the top tier of English football after being relegated from it in the 2021/22 season.
Vincent Kompany guided Burnley to finish at the top of the Championship in the recently-concluded season where they accumulated 101 points.
Now Burnley are looking to strengthen their squad in order to survive in the Premier League and they have identified O’Shea as one of their targets for the summer.
It has been claimed that they are currently in advanced talks with West Brom for O’Shea and it could even see him put through his medical paces as soon as Thursday.
The Baggies would receive a huge financial boost if they come to an agreement to sell the Republic of Ireland international to Burnley.
He has been on the books of West Brom since 2017 and he featured 41 times for the Championship outfit in the latest season.
It remains to be seen if O’Shea does undergo his medical with Burnley on Thursday, as they prepare for a competitive season in the Premier League.