Bordeaux announced on Monday a deal, reported to be €38 million, had been agreed with the Serie A side subject to a medical and personal terms being agreed.
But soon after the Ligue 1 side's statement was released, Barcelona's interest emerged and the La Liga champions moved to complete a deal worth up to €41m (£36.5m/$48m) on Tuesday.
Malcom subsequently agreed a five-year contract with the Catalan giants and sporting director Monchi is frustrated at the way Roma's planned move for the 21-year-old fell apart.
"I am very sorry for what has happened, but I believe that we had a complete agreement with Bordeaux – and then offered even more than that to get it done again," Monchi said to Roma TV.
"President [James] Pallotta made the decision to make the best offer possible, but when the negotiation became an auction we decided to withdraw from 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.
"I want to tell our fans that we are continuing to work hard, working to identify a player that wants to come to Roma and is the equal or even better than Malcom.
"Now, within the club, we are looking at our options and seeing if we have a legal case. It is true that nothing was signed, but there are many messages with the agents and their president that are at least worth being assessed."
Monchi explained Roma are unhappy with the way Bordeaux handled the deal, having wanted to keep the proposed transfer under wraps until it was official.
"What happened with Malcom is easy to explain, but perhaps a bit harder to fully understand," Monchi said. "He is a player that we liked a lot from a footballing perspective, he had the attributes that we were looking for.
"We started a negotiation with Bordeaux and the player, through his agent, more or less a week ago. After three of four days or intensive negotiations, yesterday at about 17:00 [Italian time] we found an agreement; with the agent, with the player and with Bordeaux.
"The deal was done, and we had permission for the player to travel to Rome for a medical. There was a plane scheduled to leave at 21:00 that would arrive at 23:00; everything was sorted. Because of this we were calm and collected.
"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 told him that, for us, it would not be ideal – as we are listed on the stock exchange and have to respect certain rules – but he insisted, and they ultimately did a tweet to announce the agreement.
“Because of this, we also followed up with the same statement. Everything was done, but about an hour after the announcement, there started to be suggestions of a new interest from Barcelona.
"It is true that, a few days ago, I was aware that a lot of squads were keen on Malcom – Barcelona among them. Because of this we got the deal agreed as quickly as we could: it was done. So I was very surprised when one of the representatives of the player called me to tell me that Bordeaux had withdrawn permission for the player to travel to Rome.
"I called Martin, and he told me that an offer had come in from Barcelona that was better than ours and that if we did not raise our offer we could not have the player. I told him that we had an agreement, we had made the deal, but he said that nothing had been signed and that, despite having exchanged some documents to be signed, nothing could be done."