It also suggests the 24-year-old may have been murdered.
Ms Coriam disappeared from the Disney Wonder Cruise Liner off the coast of Mexico four years ago.
Mr Matheson said: “The family have undertaken a private investigation of their own.
“I want the evidence they have found to be looked at by the people who are best qualified to do so, which is experienced British police officers.
“I will be asking Cheshire Police if they will hold a review of what has been gathered.
“If they believe there’s enough grounds for the case to be reopened I will go to the government to get them to launch an investigation.”
Ms Coriam worked as a child minder on the ship and the alarm was raised when she did not report in the morning of March 22, 2011.
Her parents, Ann and Mike, have spent more than four years campaigning for the truth .
Royal Bahamas Police Force conducted the much-criticised initial investigation into her disappearance due to where the liner was registered.
Mr Matheson said he was also pushing for a change in the law to allow UK authorities to investigate the cases of any British national lost at sea.
He said: “My mood is the same as the family’s.
“We will make sure it’s not going to go away and we are going to get to the bottom of what happened to Rebecca.”