The 20-year-old central defender has been closely followed by United since 1998, when he travelled to the United Kingdom with Boca's youth side, a team that included Carlos Marinelli, and his performances on that tour earned him a move to Middlesbrough.
United's chief scout and brother of Sir Alex Ferguson, Martin, spotted Burdisso and has been trailing the youngster ever since.
Sources in Argentina revealed that United have been in touch with Boca over the availability of the central defender, who has previously been looked at by Sunderland and Leeds United.
Unusually for the financially starved Boca, they do not seem keen on selling the Argentine Under-20 international, but president Mauricio Macri has the final say on all transfers and it seems that a bid of around $5 million from United would be accepted.
Burdisso himself, admitted that he knew nothing of United's interest and he was merely happy to continue playing for Boca.
"The truth is that I do not know anything of a transfer away from the club," said Burdisso.
"I am currently with Boca and I have only just started playing from last year."
The youngster, however, revealed that a move away does interest him.
"I am very happy and know that I still have much to learn, but to know that other clubs are interested is always very nice because that means I am doing something right.
"If something arrives and it brings me financial rewards, then I will welcome it, if not, then I will continue working hard as always."
It is being suggested that United could push through a deal for Burdisso in the near future, but if they did then they would allow him to remain with Boca on loan for at least a further six months.
Burdisso was part of Argentina's youth side which won the World Championships last year, and also included Sunderland duo Julio Arca and Nicolas Medina.
Another member of that team to be linked with United is Fabricio Coloccini, the Milan defender who is on loan at Alaves, but he has stated that no offers have yet been made.
"There are just rumours at the moment, nothing in writing" he said, speaking of reports linking him with United, Real Madrid and Barcelona.
"It is good that they have been linked, but I am concentrating on playing where I am at the moment.
"They are the best clubs in the world and one dreams of playing for them and winning things.
"But, for now, my feet are firmly on the ground and I am concentrating on being an Alaves player."
