The 21-year-old will sign with Barca for the next five seasons until the end of the 2022/23 season.
Malcom cancelled his Monday night flight to Rome, leaving expectant fans disappointed at the airport.
Monchi claims that Bordeaux caved in when Barcelona offered more money than the Italians did and as a result, the French club refused to let Malcom 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". The President said he needed the documents signed with the new offer and, when I sent it to him, he said Malcom would arrive the day after.
"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. 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.
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"Now, within the club, we are looking at our options and seeing if we have a legal case".
Media reports said Malcom's change of destination came after Barca's move for fellow Brazilian forward Willian broke down when they were unable to agree a transfer fee with Chelsea, leading them to turn to Bordeaux's fleet-footed wide forward.
Malcom, who scored 20 goals and set up 13 in 84 Ligue 1 games for Bordeaux, will join Barcelona on their U.S. tour.
Monchi does not seem a happy man and given the fact that he mentioned the messages he received from Malcom's agent and Bordeaux's president, it seems like he is willing to take legal recourse.
Malcom - who scored 12 goals in Ligue 1 last season - has developed into one of Europe's hottest talents since his arrival from Corinthians in 2016. He is Barca's second Brazilian signing of the transfer window after midfielder Arthur, 21, joined from Gremio.
They have also signed Sevilla centre-back Clement Lenglet for 35.9 million euros (£32m).
Bordeaux then met with Malcom's representatives on Tuesday to discuss the transfer which is when Roma pulled out, with the club looking to see if they have a case for legal action.