The concept of “closeness” is actually rather problematic in linguistics. English and French are “close” in the sense that they share a large amount of common vocabulary, but in the sense of genetic relationship the Germanic language English and the Romance language French are only very distantly related, namely through proto-Indo-European.
The Aramaic languages are traditionally divided (from about the 6th century BC onwards) into Eastern and Western Aramaic. Galilean Aramaic belongs to the Western branch and is thus genetically closest to the modern Western Aramaic languages still spoken (we hope, despite all the things that are happening in Syria) in just three villages: Maʿlūla, Baxʿa, and Jubbʿadīn. On the other hand, these modern Western Aramaic languages have been very heavily influenced by Arabic (with regards to vocabulary, but also phonology), unlike the language spoken in Galilee in the first century, which in terms of vocabulary is perhaps closer to less strongly arabicised languages like the Eastern Aramaic of Ṭūr ʿAbdīn in Southern Turkey. So, as I said, it all really depends on what you mean with “close”.