Despite the Clarets being relegated from the Premier League last term, the 25-year-old player still managed to impress with his performance.
Per The Mirror, Wolves and Brentford are the two teams most serious about O’Shea.
The Clarets are willing to sell, but only if they get to make a big profit on his signing.
They are said to be seeking £15 million for O’Shea, who arrived at the club a year ago.
Burnley paid his £7 million release clause to sign him from West Brom last summer.