The Bosnia-Herzegovina international was rumoured to be the Blues' top striking target in January, only for a move to collapse late in the window and Olivier Giroud to join instead.
"I am happy in Rome, with life in Rome and I don't like to look back at media rumours," he told SportsCenter. "They are sometimes true, sometimes just pumping for clicks.
"There was an offer, negotiations and I was really pleased that Chelsea wanted me. That is all I want to say about that, while I am enjoying [myself] in Rome."
Dzeko has scored more than 50 goals during his three years with Roma, 13 of which have come in the 2017-18 campaign.