The 30-year-old is a free agent after exercising an option to annul his deal with Hungarian side Mezokovesd in the aftermath of their relegation from the top flight.
The classy attacking midfielder boasts 15 caps for North Macedonia and, should he finalise a switch to Tannadice, would link up with compatriot Kristijan Trapanovski.
Talks are at an advanced stage.
Babunski, who grew up in Spain, emerged through Barca’s famed La Masia academy but didn’t play a senior match for the Catalan giants. He was a regular in their B side.
He went on to turn out for likes of Serbian giants Red Star Belgrade of Serbia (winning the league title), Botosani of Romania and Japanese big guns Yokohama F Marinos, where he played under ex-Celtic manager Ange Postecoglou.
United have made no secret of their desire to bolster their options from middle to front, and the gifted Babunski is seen as a potential coup.
Boss Jim Goodwin has already secured six signings ahead of United’s return to the Premiership, adding Will Ferry, Dave Richards, Vicko Sevelj, Ryan Strain, Jack Walton and Trapanovski.
