In Mal 4:5, 6 we have the very famous prophecy of the coming Elijah:
Behold, I will send you Elijah the prophet before the coming of the
great and awesome Day of the LORD. And he will turn the hearts of the
fathers to their children, and the hearts of the children to their
fathers.d Otherwise, I will come and strike the land with a curse.”
Thus, the Jews expected "Elijah" to appear (in some unspecified form) and thus, it was common to say, "Elijah is coming".
In Matt 17:11, 12, Jesus speaks of the expected "Elijah" and the following verse tells us the actual fulfillment:
Matt 17:13 - Then the disciples understood that He was speaking to
them about John the Baptist.
There are other places that confirm that John the Baptist was the fulfillment of the Elijah prophecy such as:
- Luke 1:17 - And he [John the Baptist] will go on before the Lord in the spirit and power of Elijah, to turn the hearts of the fathers to their children and the disobedient to the wisdom of the righteous—to make ready a people prepared for the Lord.”
Matt 11:7-11 - As John’s disciples were leaving, Jesus began to speak
to the crowds about John: “What did you go out into the wilderness to
see? A reed swaying in the wind? Otherwise, what did you go out to
see? A man dressed in fine clothes? Look, those who wear fine clothing
are found in kings’ palaces. What then did you go out to see? A
prophet? Yes, I tell you, and more than a prophet. This is the one
about whom it is written:
‘Behold, I will send My messenger ahead of You, who will prepare Your
way before You.’ [Mal 4:5, 6]
Truly I tell you, among those born of women there has risen no one
greater than John the Baptist. Yet even the least in the kingdom of
heaven is greater than he.
Even today, if an important dignitary (president king or queen) has an appointment somewhere, everyone is constantly saying, "XXX is coming" and when they arrives, "XXX is here!!". There is nothing uniquely Hebraic about this.
There is little remarkable about people expecting the fulfillment of the last great prophecy of the OT - the prediction of the :Elijah" the prophet. The problem with most people at the time was their ignorance that "Elijah", namely John the Baptist, had already arrived, and thus the disciples could say (unlike everybody else), "Elijah has come".