29-year-old Lichtsteiner is a key player for the Turin side, and has featured heavily for the club in the club's last two title winning seasons.
The player - who can operate in a number of positions - has previously been linked to Arsenal and Chelsea, although Juve are reluctant to sell given the Swiss international's performances over the last two seasons.
Prominently operating on the right-hand flank, either at full-back or as a right-sided midfielder, Lichtsteiner is known for his energy and exceptional work-rate.
United's valuation of the player fails to match that of Juventus' - something that hasn't happened for the first time under David Moyes as the former Everton chief failed with summer bids for Cesc Fabregas and Leighton Baines.
The figures reported by talkSPORT show United to be £4million short of Juve's valuation.
Lichtsteiner moved to the Old Lady after a spell with fellow Serie A club Lazio.
He had previously played for Lille and the club where he developed Grasshopper Zurich.
A regular for Switzerland, Lichtsteiner and his international team-mates have been in fine form.
The Swiss went unbeaten in their qualifying group, topping the group and supplementing their impressive campaign with friendly scalps.
Along with their World Cup qualification they have also mustered friendly wins over World Cup favourites Brazil and Germany.