At a rally in Kentucky on Monday, Trump took credit for the fact that no NFL team has signed the free agent, saying he wanted to share the news with "the people of Kentucky because they like it when people actually stand for the American flag."
"They (NFL teams) don't want to get a nasty tweet from Donald Trump," Trump said. "Do you believe that?"
Kaepernick drew national attention for his decision to kneel during the national anthem before games earlier this season.
Harbaugh, who coached Kaepernick in San Francisco from 2011 until he was fired in 2014, said he still believes in Kaepernick's ability as a quarterback.
"I think he's an outstanding player," Harbaugh, now the coach at Michigan, said on PFT Live on Tuesday. "I think he's a great competitor who's proven it in games and has the ability to be not only an NFL starter but a great NFL player.
"... Colin will be just fine. He'll just keep plugging away, and I think you'll see he'll have a great career and be a great quarterback. Win championships."
Kaepernick began last season on the bench but took over as the starter later in the season, throwing for 2,241 yards, 16 touchdowns and four interceptions with a 90.7 rating.
San Francisco (2-14) had the second-worst record in the NFL last season and holds the No. 2 overall pick in the 2017 NFL Draft.
On March 3, Kaepernick opted out of his contract to become a free agent.