Both sides are rumoured to be prepared to go head-to-head with the Premier League giants.
Llorente is valued at £8.5m by Juve, and is widely expected to leave Turin in the coming weeks following the arrival of new strikers Paulo Dybala and Mario Mandzukic.
The Spaniard has been in disappointing form over the past few seasons, with just nine goals in 45 appearances managed last term.
Nonetheless, this doesn’t appear to have deterred interest, as his signature certainly seems to be in high demand this summer.
After the departures of Radamel Falcao and Robin van Persie, United manager Louis van Gaal may remain keen to bolster his attack before the close of the window – despite having already secured five major signings.
Arsenal, meanwhile, have also heavily been linked with a new centre-forward to compete with Olivier Giroud at the Emirates – with Karim Benzema and Robert Lewandowski said to be top targets for Arsene Wenger.