The Chile international has been heavily linked with a move away from the Gunners, with Chelsea and Paris Saint-Germain thought to be potential suitors.
Giggs, who retired from playing in 2014 and then spent two years as part of the Red Devils' coaching team, has sung the praises of the 28-year-old.
"Sanchez is a brilliant player," Giggs told The Express. "His work rate, the effect he has on his teammates, a winner. He just looks how South Americans are, tough aren't they?
"Jose Mourinho bought [Zlatan] Ibrahimovic because he is a winner. He had won everywhere he'd gone. Not only the effect on the pitch but off the pitch as well. You can just feel that Sanchez would give his teammates a lift as well."
Sanchez, whose current contract expires at the end of next season, has been an Arsenal player since 2014 when he signed from Barcelona.