Sanchez is allegedly close to completing a transfer to Old Trafford, with Arsenal being prepared to sell the Chilean international due to just six months remaining on his contract.
Giggs - who has been named as the new manager of Wales - has praised the ability of the attacker, and admits that he will represent an excellent addition to Jose Mourinho's squad should the transfer go through.
The 44-year-old told Sky Sports News: "Well Alexis Sanchez is a top player. Whoever gets him or whether he stays at Arsenal, they're lucky, because he's not only a goalscorer but he makes goals, he works hard.
"So whoever gets him will be a lucky team because he is a top, top player. It doesn't happen very often does it where you're running down your contract, you've only got six months to go and you're able to get a player relatively cheap in this environment.
"But it is what it is and like I said, whoever gets Alexis Sanchez will be extremely lucky."
Sanchez will allegedly wear the number seven shirt if United secure his signature during January.