In short, no. This is one of the easiest questions to answer about the Gospels. For an introduction to the language New Testament documents see the introductory chapters of any good study Bible.
Papias
The idea of a a Hebrew original to Matthew largely originates with the fragments of a claim of Papias of Hierapolis (circa 95-110 AD) that “Matthew made an ordered arrangement of logia of the Lord in the Hebrew dialect, and everyone interpreted them as they were able”.
There is no particular reason to believe that Papias was correct, since modern scholars consider that Gospel of Matthew was – like most Jewish books designed for wide circulation of the period – composed entirely in Greek with no trace of Hebrew sources underlying the text. The idea that Matthew is a translation from Greek is not even considered in serious scholarship.
Later Hebrew Matthew translations from Latin into Hebrew
The first Hebrew versions of Matthew – such as the Shem Tov Matthew – were made in the middle ages and clearly show the dependence on the Latin Vulgate as the source text.
The Aramaic Bible
The main translation of the New Testament in the non-Greek speaking Christian middle East was the Peshitta, a translation from Greek into Syriac, a variety of Aramaic. The legend later developed in the Syriac-speaking Assyrian church – partially as a product of theological competition with the Greek-speaking Roman Eastern and Orthodox churches – that the Syriac New Testament was actually the original, and the Greek a translation from the Syriac.
No respected New Testament scholar has ever taken this claim seriously, and it is now admitted to be false even by modern scholars in the Assyrian church. However when a member of the Assyrian church, George M. Lamsa, published a translation of the Syriac Peshitta into English (1933) his translation – and Lamsa’s presentation of the Assyrian church’s claims for “Aramaic primacy” – gained some popular traction in English speaking countries.