The Serie A side were hoping to find out if they had a chance of signing Sanchez, initially on loan, by the middle of this week.
But 30-year-old Sanchez’s £390,000-a-week salary is proving to be problematic as Inter are only prepared to pay less than half of the amount.
United view this offer as unacceptable, while Sanchez himself wants to leave.
The former Barcelona and Arsenal player is looking to link up again with his friend and former United striker Romelu Lukaku – but he is thought to be loath to accept the kind of significant wage cut that would make the move easier to complete.
Inter remain keen on the Chile forward, who has had a hugely disappointing time at Old Trafford, scoring just five goals in a season-and-a-half. Sanchez scored as many times for his country at the Copa America this summer as he did through the entire 2018-19 campaign.
Unless United manager Ole Gunnar Solskjaer has a change of heart, Sanchez, who played alongside Matteo Darmian, Chris Smalling and Phil Jones in a closed doors friendly against Sheffield United on Tuesday, is only likely to be involved in United’s Carabao Cup and Europa League campaigns this season.