According to BBC Sport's Simon Stone, the Nerazzurri are putting together an offer, and United are open to letting him leave.
Di Natale told Gazzetta dello Sport (h/t Goal's Sam France):
"Sanchez to Inter would be an extraordinary coup and a gamble that both parties could win comfortably.
"Alexis is an exemplary professional, someone who always arrived early for training sessions and never held back during a match."
The former striker, who played with Sanchez at Udinese from 2008 to 2011, said the Chilean retains an "excellent reputation" in Italy. He added:
"He has all the ingredients needed for a great season. Alexis needs people to have faith in him and I am sure he'll do well with [Inter boss Antonio] Conte. I think he had some fitness problems over the last 18 months and he certainly had difficulty settling in at Manchester United."
After United's 1-1 draw with Wolverhampton Wanderers on Monday, manager Ole Gunnar Solskjaer said the forward could leave the club this summer:
Red Devils legend Gary Neville is hoping the club will move him on:
The 30-year-old arrived in January last year and has scored just five goals in 45 appearances.
He found the net just once in the Premier League last season, which football writer Richard Jolly put in perspective:
With Sanchez said to earn in the region of £400,000 per week, the club haven't nearly received the return they had hoped for on their investment.
Despite that, Bleacher Report's Rob Blanchette want him to remain at Old Trafford this season:
Rob Blanchette @_Rob_B
Sanchez is on a crazy wage for someone who has failed to contribute. But I'd rather see #MUFC retain him this season and try and get something out of him. He looked good for Chile at the Copa America. There's a player in there somewhere. His experience could be vital this term.
Sanchez offered up 47 goals and 35 assists in 141 appearances for Barcelona before producing 80 and 45, respectively, in 166 games at Arsenal.
United can't afford to keep him around if he's not contributing, but they'd have an incredible asset if he can get back to peak levels. What's more, after allowing Romelu Lukaku to join Inter, the Red Devils would only have forwards Marcus Rashford, Anthony Martial and Mason Greenwood if Sanchez were to leave.
A move away from Old Trafford could be what Sanchez needs to reignite his career, though. If United aren't confident he can do so with them, his move could be best for all parties.