He also claimed that Roma upped their offer but were asked to increase it further and as they did not want to enter into a bidding war, they pulled out of the deal.
Roma sporting director Monchi said "nothing was signed" with Malcom, who had also been linked with a move to the Premier League, with Arsenal, Everton and Tottenham said to be interested.
Malcom featured 36 times last season across all competitions, scoring 12 goals and registering seven assists.
Roma fans waited for Malcom at the airport - and then Barcelona swooped.
"The agents and the Bordeaux president told me that if all was agreed, today [Tuesday] we would be able to exchange the documents and the player would again be authorised to travel to Rome in the evening".
"I told him we had an agreement, but he told me we hadn't signed anything".
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"Once we found the agreement with Bordeaux, about 30 minutes later their president, Stephane Martin, called me to tell me that there were a lot of rumours surrounding the deal, and for them it would be better to make an official statement".
"I informed [Martin] and [Malcom's] agents that Roma were ready to beat Barcelona's offer".
Malcom, who has yet to represent his country at senior level, began his career in his homeland with Corinthians and was part of the Campeonato title-winning side of 2015 before moving to France in January 2016. That was against my opinion, but he insisted he was willing and said, "Go for it". If someone wants to come to Roma that is great, but ultimately if they do not want to come to Rome then we do not want them.
Malcom passed a medical at Barcelona on Wednesday and will head to join up with his new teammates on their pre-season tour in the US.
"President [James] Pallotta made the decision to make the best offer possible, but when the negotiation became an auction we chose to withdraw from it". Early this morning I spoke with Malcom's agent, Fernando Garcia, who had a meeting with Bordeaux planned at 12pm to confirm everything was in place for the player to travel to Rome in the evening.
Brazilian soccer player Malcom Filipe Silva de Oliveira poses in front of an FC Barcelona logo at their offices next to Camp Nou stadium in Barcelona.
Malcom is Barca's second Brazilian summer signing, after midfielder Arthur, 21, joined from Gremio for £35.5m.