I think the Greek sentence could mean either (the person you are looking for) is not me or I am not myself (today).
The English counterpart sounds off to me.
Agreed. And the first one would not be "Λυπάμαι, δεν είναι εγώ."—as "sorry, it's not me" would in English?
I expect that in Greek, when somebody says to you Are you the person I am looking for? the proper answer would be δεν είμαι εγώ, even though the word-for-word translation into English is awkward.
"Δεν είμαι εγώ" is the correct answer in that situation. "Δεν είναι εγώ" sounds wrong, however close to the EN one it is.