The Red Devils were heavily linked with a deadline-day transfer for the Frenchman, having missed out on their top target Jadon Sancho.
France Football claims that United had agreed terms with Barcelona over a switch and sent all of the relevant documents to the players by 6pm on October 5.
The agreement would have allowed a domino effect of other transfers to take place, with Barcelona set to replace Dembele with Memphis Depay and Lyon to replace Memphis with Leicester City's Islam Slimani.
All of the paperwork for those deals was also reportedly in place by 6pm, but they collapsed due to Dembele's refusal to leave Barcelona.
The 23-year-old informed the Spanish giants that he had no intention of leaving at 8pm on October 5, just three hours before the deadline.