I think both are possible in the English-speaking world. In an interchangeable kind of way, I think.
In my country, however, it would be pronounced as del-FEE-niss only. The 'y'-pronunciation is something typically English. In my country, an 'i' either gets pronounced as the 'i' in the English word 'hit', or as an 'ee' like in names such as
Nadine.