West Ham boss Manuel Pellegrini managed the Roma marksman at Manchester City once upon a time.
The Irons only have a handful of striking options but, apart from Marko Arnautovic, none are overwhelming, with Javier Hernandez and Andy Carroll there.
But some West Ham fans on Twitter would love to see the Bosnia & Herzegovina marksman in East London as their competition next term.
Here's how they reacted:
Take him— jimmy b (@jimsblacktaxi2) April 16, 2019
Yes please— Joseph Walsh (@walshy1895) April 16, 2019
@WestHamUtd Buy Džeko please, we need him so bad, plus I want to get džeklan on the back of my West Ham shirt— Cat Daniel (@HarryButler69) April 16, 2019
Seriously I would take him all day long. We can still invest in a young striker. Looks like Carroll has gone so like for like the difference will be he will play 75% of the games whilst Andy played 5% of the games. Take him and Maxi Gomez. Sorted!— Dave Bilston (@DbBilston) April 16, 2019
He's better than anything we've currently got— Geoff ⚒ Lockwood (@geoffl65) April 16, 2019
Oh yes please— ⚒Linh Blunden⚒ (@linhblunden) April 15, 2019
We should have got him a year ago - still a decent striker and PL savvy— Clive Osgood (@1ossieosgood) April 15, 2019
Džeko is a serious player will be great signing for anyone, especially West Ham— Ben (@BenMcLennon) April 17, 2019
Considering we’re upgrading massively on Andy Carroll I’m not bothered.— Jay (@ReggyWallaceWHU) April 16, 2019
Dzeko, who is contracted to the Italian giants until 2020, has netted only eight goals in 27 Serie A outings this season.
He might be winding down a little, but few would argue that he isn't still a better striker than Carroll and Hernandez.