Sanchez has endured a miserable time at United since he joined from Arsenal in January 2018 in a deal that saw Henrikh Mkhitaryan move to the Gunners.
He has scored four goals in 32 Premier League appearances for the Red Devils, with his spell at Old Trafford heavily affected by various injuries.
Inter are reportedly keen to sign Sanchez on loan, which would allow the Chile international to reunite with his former United team-mate Romelu Lukaku.
While Solskjaer was unwilling to give firm details about the status of a potential move for Sanchez, he accepted the 30-year-old may depart before the European transfer deadline on September 2.
"There's still a couple weeks left of the transfer window," Solskjaer said after Monday's 1-1 league draw away to Wolves.
"There is a chance [he could leave]. Some clubs have shown interest in Alexis and we'll see what happens.
"We can't update you more than that."
While Sanchez's time at Old Trafford looks to be coming to an end, fellow forward Anthony Martial has started the 2019-20 season in fine form.
The France international hit the opening goal of the game at Molineux to reach 50 in all competitions for United and Solskjaer hailed his impact.
"He's scored two in two now and he'll only improve," Solskjaer said of Martial. "The relationship between him and Marcus [Rashford], Jesse [Lingard] and the other forwards will only improve.
"The more we get him into positions to score, the more he will. He's more between the posts so I'm happy with that.
"It was a wonderful goal."
United were denied the three points that would have taken them top as Rui Patricio saved Paul Pogba's second-half penalty after Ruben Neves had cancelled out Martial's effort.