Dzeko is on loan with a view to a permanent transfer. I don't know if they have to buy him like Valencia had to buy Negredo, but he is definitely on loan at the moment
However, I think he can play against us. Courtois was on loan from Chelsea to Atletico but UEFA said Chelsea could not prevent him from playing against them
He is a Roma Player.
After months of speculation during the 2015 summer transfer market, Džeko officially signed for Italian club Roma on 12 August 2015, on a €4 million loan with an €11 million option to buy that becomes mandatory after certain performance related goals are met.[58][59] These clauses were activated on 1 October 2015, making Džeko a permanent member of Roma.[