The Bosnian forward has emerged as the Premier League title holders top target to add some more attacking power at the west London club.
Chelsea have been linked with surprise targets during the current transfer window, but Dzeko would be a more natural fit for the Blues given his previous experience at Manchester City.
Dzeko won two Premier League titles, the FA Cup and the League Cup during his four and a half season spell at The Etihad.
Summer signing Alvaro Morata has struggled with confidence and a loss of form in recent months to heap further pressure on the £58m striker.
Former Arsenal midfielder Merson has endorsed Chelsea FC’s pursuit of the Bosnian striker, adding that Dzeko would be a suitable rival for Morata.
“Go and get Dzeko for £30m. He won’t be a stop gap,” Merson told The Debate on Sky Sports on Thursday night.
“If he starts well, he gets in the team. He will compete with Morata.”
Chelsea FC have won the Premier League title in two of the past three seasons under Jose Mourinho and then Conte.
Diego Costa was a key part of both of those title successes after he netted 20 times in both the 2014-15 and 2016-17 seasons.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news