The Brazilian has seen both north London clubs closely linked with an approach in recent weeks, with a transfer possible as early as this current transfer window.
For their part, Bordeaux have played down the talk, insisting there has been no official contact for their gem.
But Malcom confessed that he would love to star in the English top flight while refusing to confirm his future in Ligue 1.
"I don't know [if I will go]. If I do leave, that would be fine," he explained to reporters after Bordeaux's 1-0 defeat of Nantes on Saturday.
"I will be grateful to Bordeaux, that's life. If I have to stay I will, and I will do my job. It is true that England is a dream for every player."
Bordeaux director Nicolas de Tavernost, meanwhile, underlined his club's desire to keep Malcom until the end of the season.
"We don't want him to go, he will be at Bordeaux for the second half of the season," the businessman said.
"We think he could leave this summer if the club find the right offer, but right now we need him."
Goal understands that Arsenal have pulled out of the race to sign Malcom in the January window, although would be willing to discuss a transfer in the summer.
Arsene Wenger's side are not willing to pay the French club's £44 million asking price for Malcom but do remain confident they could strike a deal at the end of the season.
The Gunners have prioritised the signings of Henrikh Mkhitaryan and Pierre-Emerick Aubameyang, with both players having now agreed personal terms, and believe that the experience the duo possess can push them further up the Premier League table in the chase for a top-four spot.