CNN first reported Tuesday that Laurean had briefly stopped by Ramos Ramirez's liquor store in Zapopan, just outside Guadalajara.
Days later, Ramos Ramirez saw a television report that Laurean was wanted in the United States for killing 20-year-old Lance Cpl. Maria Lauterbach.
"We were completely shocked," he said.
Authorities have said they suspected that Laurean had fled to Mexico, but the comments from Ramos Ramirez were the first public confirmation that the Marine had been in the country.
Mexican and U.S. officials said they were looking into the report, but didn't have any more information.
The Marines first began searching for Lauterbach on Dec. 17, after Lauterbach failed to show up for work. Local authorities took up the case Dec. 19, after her mother reported her missing. Three weeks later, officials found Lauterbach's burned remains in a fire pit in Laurean's back yard.
Lauterbach had earlier accused Laurean of rape. Authorities are trying to determine if Laurean, a 21-year-old from Las Vegas who is married with an 18-month-old daughter, was the father of Lauterbach's unborn child.
Ramos Ramirez said he didn't contact police about his cousin because he believes Laurean is innocent.
"It didn't seem right to contact police," he said. "He is a normal person, with no tendency for doing bad things."
He said police still hadn't contacted him about his cousin late Tuesday, despite the international manhunt.
Jalisco state officials said they hadn't been formally notified of Laurean's warrant.
Ramos Ramirez said Laurean and most of the Marine's family moved to the U.S. more than 10 years ago, and he had seen Laurean only three other times since. The second time, five years ago, Laurean came for vacation and spent a few days with Ramos Ramirez's mother, Maria Ramirez.
Ramirez was with her son when Laurean walked into the liquor store last week.
Laurean hasn't contacted any other family members in Mexico, Ramos Ramirez said.
He said Laurean didn't stay long, and didn't say anything about why he was in Mexico or where he was headed. Ramos Ramirez said he wasn't surprised by the brief trip because Laurean isn't very close to relatives in Mexico. He added that his cousin seemed calm.
"It was like any visit," Ramos Ramirez said.
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Associated Press writer Traci Carl contributed to this report from Mexico City.
