The Fury family's relationship with a major Irish crime boss is what's keeping Tommy from entering the United States ... with U.S. officials placing a travel ban on any fighters, managers and promoters with ties to the wanted man.
Daniel Kinahan -- who helped found the MTK Global boxing promotions company that previously repped Tyson Fury -- is accused of running a massive drug and firearms trafficking operation in Europe ... and is currently on the run from authorities.
Law enforcement sources tell us fighters with any association with Kinahan -- even the most tenuous ties with the guy -- are being barred from traveling as part of the federal investigation .