The superstar has been the subject of intense transfer speculation in recent days with his Paris Saint-Germain future in doubt.
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However it appears Real Madrid will be his destination rather than Old Trafford.
Brailsford, who is Director of Sport at new investors Ineos, was asked if he could sign Mbappe.
He replied with a cheeky grin, saying: “I don’t think so, he’s probably off to Real Madrid ain’t he.”
Mbappe, 25, could reportedly become a free agent this summer after deciding to quit PSG.
He came close to leaving for Real Madrid two years ago before penning a new deal.
But that contract extension comes to an end this summer and the Frenchman has chosen not to renew.
Mbappe is understood to be “leaning towards” joining Real with the Spanish giants eager to strike a deal.
But his representatives have been left “unconvinced” by their offer.
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That could allow other clubs to swoop with Arsenal said to be an interested party – a move believed to be of interest to Mbappe as he could follow in the footsteps of his hero Thierry Henry.
Mbappe also attracted interest from Saudi Arabia last summer with reports claiming PSG accepted a £259million bid for the forward from Al-Hilal.
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