The Red Devils are widely expected to bring a new centre-back to the club this summer and have been strongly linked with a swoop for Leicester City's Harry Maguire.
However, according to Turkish Football, United have now made a surprise enquiry for Demiral, who could find it difficult to secure regular minutes at Juve during the 2019-20 campaign following the arrival of Matthijs de Ligt.
Demiral only joined Juve from Sassuolo earlier this month after impressing on loan at I Neroverdi in the second half of the 2018-19 season.
The 21-year-old - a four-time Turkey international - could be available for £35m this summer, which would be significantly cheaper than any deal for Maguire.
Ole Gunnar Solskjaer's side, who will continue their preparations for the new season against Inter Milan on Saturday, have already signed Daniel James and Aaron Wan-Bissaka in this summer's transfer window. body check tags ::