Sanchez, United's highest-earning player, has failed to justify his hefty salary since joining on a free transfer from Arsenal in January 2018.
Solskjaer had recently expressed confidence that the Chilean would stay at Old Trafford beyond the close of major European transfer windows on 2 September.
But the United manager confirmed after a 1-1 draw with Wolverhampton Wanderers on Monday night that Sanchez could be allowed to leave if an acceptable offer is received.
"There's still a couple of weeks left of the transfer window and there is a chance," he said.
"Some clubs have shown interest in Alexis, so we'll see what happens. I can't update you more than that."
Sanchez is yet to appear for United this season having played at this summer's Copa America with Chile and missing his club's pre-season tour through injury.
The 30-year-old has scored just five goals in 45 appearances for United since his high-profile arrival more than 18 months ago.