The veteran defender announced earlier this week that he will leave Camp Nou at the end of the season after spending his entire career with the Blaugrana.
The Frenchman, who left Catalunya after three years alongside the Spain international, would be happy to see his old colleague join him in North America.
"If he wants to come and play in America, he would be welcome," the former Arsenal captain told ARA. "If Puyol comes, it would be great. It would be good for the league and it's always good to have players like him."
However, Henry said that he has not been in contact with the 35-year-old in an effort to lure him across the Atlantic Ocean.
"He is a very intelligent and reliable man who already knows what he wants," he added. "We must respect his decision and we have to enjoy the last few months he has in a Barca shirt. He's an example for the team and club."