The Red Devils managed to see off competition from defending Premier League champions Manchester City to sign Sanchez in January.
The 29-year-old made a slow start to his Old Trafford career following a return of three goals in his opening 18 games for the Red Devils.
Sanchez’s poor form has rumbled on into the new season and the Chile international has failed to score in his last five games.
The former FC Barcelona forward scored 80 goals in 166 games during three and a half seasons at Arsenal.
Sanchez established himself as one of the best players in the Premier League during his spell at the north London side.
Former Manchester United winger Giggs is confident that Sanchez can find his form at the 20-time English champions.
Giggs told Sky Sports: “I’m a big fan of Sanchez, I was a big fan of his at Arsenal and sometimes it just takes players a bit longer to settle in – even though he’s a top player he just looks like he’s a bit short of confidence, but I’m sure he’ll come good as he’s a top goalscorer and a good player as well.”
He added: “He can play anywhere across the front, he played on the right for Barcelona and up front in his better days for Arsenal. I’ve seen him just off the left the most for United so it just depends who he’s playing with and who they’re playing against.
“He can also play that No 10 role but I think the best performances I’ve seen from him at United are just coming off the left, but it’s just not quite happening for him at the moment.”
Manchester United finished in second spot in the Premier League table last term but ended the campaign without silverware.
The Red Devils lost to Championship side Derby County on penalties in the League Cup third round on Tuesday night.
Manchester United will take on West Ham United at the London Stadium on Saturday afternoon.
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