Celtic boss Ronny Deila says keeping his best players will take priority over acquisitions in the transfer window.
Chelsea striker Fernando Torres is understood to be set for a return to Atletico Madrid, according to Sky sources.
Jutkiewicz has been linked with a host of clubs this summer amid uncertainty over his future, but it is believed that Burnley could be about to win the race for his signature.
The newly-promoted Premier League club had considered turning their focus to other targets but retained their interest in Jutkiewicz and it is understood that he is set to sign a three-year deal at Turf Moor.
The 25-year-old has been at Boro since making the move from Coventry City in January 2012, but fell out of favour midway through last season and was loaned out to Bolton Wanderers.
Bolton were among the clubs reportedly keen to land Jutkiewicz during this transfer window, along with Derby County, Wigan Athletic and Wolverhampton Wanderers.