The Serie A club had wanted to bring the 6ft 2in Scottish under-19 international to Italy on loan with a purchase option. The Hoops rejected the offer since Welsh has established himself as a defensive staple since breaking into the first squad last season. Last season, the 21-year-old was handed a baptism of fire with an Old Firm debut followed by a Europa League start against AC Milan, and he kept his position in the club for 21 outings, with 19 more under Ange Postecoglou in the first half of this season.
With Aaron Hickey having a standout season at Bologna and ex-Celt Liam Henderson at Empoli, Udinese, who are presently 14th in Italy's top flight, were seeking to make Welsh the third Scotsman in the top flight.