The young winger is regarded as one of France's brightest prospects and Chelsea have been monitoring him since 2007.
United, Inter Milan, AC Milan and Arsenal have all been linked with Obertan too and Triaud believes the Barclays Premier League champions will win the battle for the 20-year-old's signature.
"It's actually a great possibility," he told L'Equipe. "United want him and we would be delighted to see Gabriel develop in such a club.
"We will make it official when the moment comes."
Obertan, who spent the second half of last season on loan at Lorient, is a regular in the France Under-21 side and scored against England U21 in March.
He was awarded the Most Valuable Player award at last month's Toulon International Youth Tournament.
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The Man frae Govan (06/07/2009 at 10:05)
Personally I prefer this strategy to buying big name stars - look at international teams - full of stars but never play as a team. I still think ourselves and our Catalan friends will be at the top of the tree come May.