The case threw already cool U.S.-Cuba relations into a deep freeze, although there have been signs of some thawing this year.
Jackson has traveled to Yugoslavia, Syria and Iraq in the past to help gain freedom for U.S. citizens jailed there.
In March 2011, shortly before Gross' trial, he appealed to Cuba to release the man on humanitarian grounds and offered to help mediate.
Former President Jimmy Carter came to Havana later that month, but left without Gross.
In September 2011, the former governor of New Mexico and U.S. Ambassador to the United Nations, Bill Richardson, made a high profile visit to try to negotiate Gross' release.
But the trip abruptly fell apart amid mutual recriminations as Richardson wasn't even allowed to see Gross, and referred to him in public comments as a "hostage."
Jackson has visited Cuba on several occasions and met with both former President Fidel Castro and current President Raul Castro. In 1984, he helped negotiate the release of 26 Cuban prisoners. Most of them went into exile.
On Friday, Jackson said he hopes to help continue healing the wounds of a five-decade divide between islanders and exiles.
"It's good to be back to Cuba again," Jackson said. "We've been here over the years. We have developed kinships with many Cuban-Americans trying to build Cuban-Cuban American family reunification."
"We hope for the day we will have the walls down, the bridges built," he said.
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Peter Orsi on Twitter: www.twitter.com/Peter_Orsi