Messam, of the Edmonton Eskimos, was the league's third-leading rusher this season with 1,057 yards on 195 carries and six touchdowns. The Toronto native was named the CFL's Outstanding Canadian Player of the Year.
Eskimos general manager Eric Tillman told the Journal that the Dolphins and Messam were close to a deal.
"Yes, it's true," he said. "(Dolphins GM) Jeff Ireland phoned me late (Saturday) afternoon and said they had decided to offer Jerome a contract, but their proposal would not include a signing bonus."
Tillman added that Messam's agent had told him the running back "would be accepting the offer from Miami," though the newspaper also cited Eskimos executive Dave Jamieson, who cautioned that the deal is not official and thinks "there is work to do on the bonus."
Messam entered the CFL in 2010 after attending Graceland University in Iowa and became the first Canadian running back in 12 years to break the 1,000-yard mark last season.