Normally we would just say "my friend". If you want to make it clearer that the identity of the friend has not yet been specified (particularly in this conversation), you can say "a friend of mine" or "one of my friends". In special contexts, you can say things like: "he has been a good friend to me". Note this uses "to" and not "of". The emphasis here is on the behaviour of that person (the person who has been a good friend to you), and not so much on the mutuality of your friendship. Possibly someone could be a good friend to you with you really being a good friend to them, in which case it is doubtful whether you are really "friends", but that person has behaved as a good friend would.

It's "a friend of mine" or you can simply say "my friend."

a friend of mine

“A friend of mine” is correct. This “double possessive” may seem illogical, but it is a feature of English. The supposed explanation is that it is a type of partitive, but other Western European languages do not use this. The same goes for the use of the ’s suffix: “A friend of Jonathan’s” is correct. Note that there are exceptions — if we’re not really talking about possession, we don’t use the possessive: “A photo of me” (my image is in the photo) versus “A photo of mine” (a photo belonging to me or taken by me, regardless of the contents of the picture).

A friend of mine or my friend. :)