However, the United States can block the process because it has already sought Rocha's extradition in its own wide-ranging case.
Swiss justice department spokesman Folco Galli said American officials must consent before Rocha can go home.
"It will then be for the US authorities to state whether or not they agree to Nicaragua being given priority," Galli said in a statement.
If American officials refuse to give up their claim on Rocha, the Swiss justice ministry will decide which extradition request to grant, Galli said.
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He is suspected of taking bribes from marketing agencies which were awarded tournament broadcasting rights in South and North America.
"The Nicaraguan criminal prosecution authorities, like their US counterparts, suspect Rocha of having abused his office for personal gain," Rocha said.
Rocha was among seven football officials, including two then-FIFA vice presidents, who were arrested in dawn raids in May.
Requests to extradite Rocha and five other men who have resisted being sent to the U.S. Are being processed by Swiss authorities.
Decisions are expected within weeks but can be appealed to Swiss federal and supreme courts, delaying the process by several months.