The young full-back had been linked with a temporary switch away from Old Trafford to gain some more game-time.
Williams played nearly 70 minutes of the Under-23s' pulsating 6-3 win over Liverpool on Saturday afternoon and Ole told reporters at his press conference, following the first team's draw at Arsenal, that the 20-year-old will be staying put.
“Brandon will stay,” declared Ole. “He played for the 23s against Liverpool for some match fitness.
”He's been working really hard and we don't have any more players that we feel will be going.
“Brandon has been really good lately, working really hard in the last few months and he's ready when the chance comes.