Falcao has endured two torrid Premier League loan spells in recent seasons, first failing to make an impact at Manchester United last season before before joining Chelsea.
The champions are reportedly keen to terminate the Monaco striker's stay in January, but few teams look willing to offer the Colombia international a new home.
During his time in England the formerly deadly forward has scored just five goals in 40 appearances, but Valeri – who Falcao played alongside at Porto but who now features for MLS champions Portland Timbers – hopes he will soon make a move to the United States.
“I would love it if he decided to join the MLS,” he told reporters.
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“I’m convinced, because of the relationship we have, that Falcao would like to live in America and test himself in the MLS.”
Another pal of Falcao, Columbus Crew’s Federico Higuain - who played alongside the Colombian at River Plate - has also lavished praise upon the 29-year-old.
“He could play at the top level in the MLS,” he added.
“Now we wait to see what his choice will be. Sometimes your team helps you because they are playing well – sometimes the opposite occurs. But we are still talking about a fantastic striker.”