Blind was linked to a move to the Italian side towards the end of the month after they lost left-back Emerson Palmieri to Chelsea.
Father Danny stated on deadline day that Roma wanted to take 27-year-old Blind on loan, but the Red Devils were hoping for a permanent sale.
Roma brought left-back Jonathan Silva on loan from Portuguese club Sporting instead, and Monchi insists the Argentine was always the preferred candidate instead of Blind.
"We talked with Jonathan Silva even before the window opened, in expectation of Emerson leaving," Monchi told reporters.
"Blind was offered to us three or four days ago, but we decided he was not the right player, even from an economic point of view, which is important."
Roma were reportedly in danger of losing their highly-rated goalkeeper Alisson as rumours of a late bid from Liverpool spread.
However, Monchi denied claims that an offer was made.
"No, no," he replied to a question on a bid for Alisson. "Now let me rest for a week before we start talking about the next transfer period."