England international Chilwell joined Chelsea last month for a handsome £50m after much talk about him leaving Leicester.
United were thought to be one of the club’s eyeing a move for the 23-year-old.
But the MEN claim that the Red Devils called off their pursuit of Chilwell last November as they no longer felt like they needed to strengthen in that position.
The report suggests that United felt they had a more than adequate back up option in Williams to then-first choice left-back Luke Shaw.
Williams enjoyed a superb breakout season at Old Trafford last term, starting 11 Premier League games, and even filling in at left-midfield at times.
His efforts were rewarded with a new four-year contract in August, and the England youth international admitted that it was his dream come true to be playing with the first-team every week.
“Signing this contract is another really proud moment for myself and my family,” Williams said.
“Having been at Manchester United since I was seven years old, it’s genuinely a dream come true to be playing in the first team.
"It's taken a huge amount of hard work to reach this point and been really special for me to break through into the squad.
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"I’ve learned a lot throughout the season from the manager, his coaching staff and my team-mates and I want to repay the trust that they have all shown in me.
"I know that everyone at the club is working really hard every day to achieve success in the coming years and I am really excited to be a part of that.”