The Italian hit-man has emerged as a target for both sides in recent weeks after making a fine start to the Serie A campaign.
The 23-year-old has long been considered a top talent, as his record of four goals in 10 league outings has attracted interest.
The player himself has also opened the door for a switch to English football, leading to speculation that £20m offers may be enough to lure him away from Rome.
However Sabatini – Roma’s director of sport – has quashed such talk by insisting that Destro is too valuable to the club to be sold:
“We’re happy with the roster we have, but we’re always monitoring,” he is quoted by the Daily Star.
“Destro is off the market as far as we are concerned, we consider him a top player and therefore he won’t leave.”
Destro was a youth player at Inter Milan before moving to Genoa.
But he really emerged as one Italy’s top youngsters during his stint at Siena, whom Roma paid around £6m to for his signature in 2012.