Boro forward Jutkiewicz has attracted a lot of interest this summer as uncertainty continues to surround his future, and Burnley are among those keen to sign him.
However, the Premier League new boys have been frustrated by Middlesbrough's demands for the 25-year-old and may pull out of the race for his signature.
Burnley are considering other players and it is understood that they are ready to switch their attention to Sunderland's Danny Graham.
Graham is expected to leave Sunderland and Middlesbrough are among the clubs reportedly eager to sign him, but Burnley are also monitoring the situation.
Sean Dyche is a fan of Graham after working with him at Watford and could make a move after failing to agree deal with Middlesbrough for Jutkiewicz.