The 25-year-old Republic of Ireland international was rumored to have rejected an offer from Ipswich Town.
However, now The Sun claim that he is set to make the move for around £10 million.That claim is being denied by TWTD, which is said to have sources close to Ipswich.
The outlet states that O’Shea is very much content to remain with the Clarets for this season.
Burnley were rejected to the Championship from the Premier League, while Ipswich went the opposite way.