In 2016, Trump earned 8 percent of the black vote compared to 89 percent for Hillary Clinton. Scott told "The Story" host Martha MacCallum that he has seen polls showing the president with 30 percent support from African-Americans.
"He can be between 14 and 16 percent in 2020," said Scott, who added that such a result would be "pretty phenomenal -- game over."
Scott became the first African-American Republican senator elected from a Southern state since Reconstruction. The first two African-American senators were both Mississippi Republicans from the 1870s -- Blanche Bruce and Hiram Revels. Since that time, most African-American senators have been Democrats, and most Democratic presidents have enjoyed overwhelming support from that voting bloc.
Scott also said Tuesday's State of the Union will remind all Americans of the achievement of the Trump administration.
He noted that unemployment figures have gone down and the "bottom 20 percent" of wage earners are getting higher raises than those in the upper 20 percent.
"We're talking about somebody who is producing amazing results," he said. "He's actually in the middle of one of the best runs a president has had in my lifetime."
Fox News' Adam Shaw contributed to this report.