The Bosnian forward is thought to be closing in on a potential move to the defending Premier League champions in the January transfer window.
Chelsea were previously linked with a move to sign West Ham striker Andy Carroll and Stoke City target man Peter Crouch.
The west London outfit have now appeared to settle on Dzeko their top target to strengthen Antonio Conte’s attacking options for the remainder of the 2017-18 season.
Chelsea summer signing Alvaro Morata has struggled with confidence and fitness issues over the past number of weeks.
The £58m signing has only scored two goals in his last 10 games and Morata failed to find the net in their last six games in all competitions.
Morata was sent off in Chelsea’s penalty shootout win against Championship side Norwich City in the FA Cup third round replay at Stamford Bridge to further compound his misery.
Former Chelsea winger Nevin believes Dzeko would be a great addition to the Chelsea team and prove a worthy competitor for a first-team spot with Morata.
“Morata had a brilliant start,” Nevin told Irish radio station Newstalk. “He had a phenomenal start. He had no-one to give him a rest.
“The goals weren’t coming from Batshuayi. If they can bring Dzeko in, it would make utter sense.
“It would be a real battle short term who would get the start. It would make perfect sense.”
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