The Roma striker has been linked with both Crystal Palace and West Ham.
The 24-year-old forward spent the second-half of last season on loan with AC Milan, and it is believed that he will be available for transfer this summer, with no future at Roma planned.
Rudi Garcia is said to not be keen on the Italian international, and Palace see this as an opportunity to add to their striking ranks.
London24 claimed earlier this week that West Ham are also interested in him, whilst indicating that he is valued at roughly £10.6 million should any team look to purchase him outright.
The eight-capped Italian international played 33 games last term - in spells with both Roma and Milan - scoring eight goals. Whilst not a great return, he was frequently utilised in only a substitute capacity, and netted all his goals when starting games.
Would Palace be wise to move for Destro?
The attacking areas are arguably the weakest positions in Palace’s squad, with Glenn Murray ending the season as first-choice striker. Although he impressed, he turns 32 next season, and the Eagles should be looking to upgrade him with a younger player to oversee the move from established Premier League side to top half challengers.
It is expected that the likes of Dwight Gayle, Marouane Chamakh and even Murray himself will leave this summer, and Destro would be a signing of real intent from Palace, showing they mean business next season.