A report in Spain claimed Braithwaite had brought up the prospect of taking on the iconic jersey in negotiations with the Blaugrana.
Messi has informed Barca of his desire to leave Camp Nou, with Manchester City widely linked with a stunning move for the Catalan club's greatest ever player.
But Braithwaite insisted he made no such demand and called the mere suggestion "so disrespectful".
"What do people think themselves? Of course I did not go to the club and ask for Messi's number," he told Danish newspaper BT. "It would be so disrespectful.
"I really feel that the people who come up with these kinds of stories lack respect for a lot of people.
"A lot of things are being written about Messi and I do not know what is happening. I can only say that he is a great player and person to be team-mates with.
"It goes without saying what he can do as a football player when he shows it every weekend. He is one of the best players ever and, of course, it will be a loss for the club if he disappears.
"I hope it does not happen, but I do not know what is happening, so I do not want to comment on something I do not know anything about."
Braithwaite is more certain of his own future at Barca, having signed a contract until 2024 when he joined from Leganes in February.
"There are, of course, a lot of rumours," he said. "Our whole team has been linked away, so it's only natural that I, too, have been linked.
"This is how it is to play at Barcelona when you do not achieve the club's goal."
Braithwaite said: "I have a contract for four more years with Barcelona.
"I'm having a great time at the club and they're happy with me, it seems, so I have a really good sense of where I am.
"To be honest, I have not had any talks about changing clubs with anyone at all. You're the first one I talk to about it, because I have not had a single thought about it at all.
"I'm just thinking about how to prepare to play well for Barcelona next season. I'm insanely hungry to get out next season and win a lot of titles."