Sanchez completed a high-profile switch from Arsenal earlier this week and is in line to make his competitive bow for the Red Devils against Yeovil Town on Friday night.
The 29-year-old has already caught Shaw's eye on the training ground, however, and the left-back is now excited to build up a strong rapport with the latest Old Trafford arrival if they are used in tandem down the flank.
"It was quite surprising at the start because obviously he wasn't linked with us at all and everything moved really quickly," he told Flow Sports Premier. "But really happy, obviously he's a phenomenal player.
"One of the best in the world, the quality he'll bring to the side will surely boost our attacking threat. We've already seen his quality in training and some of the things he's done is a joke."
Sanchez, handed the number seven shirt at United, is reportedly earning £505,000 a week in wages.