Matthews posted a message and a photo on Instagram ahead of the Titans' home game against the Houston Texans at Nissan Stadium on Sunday:
Kaepernick has remained a free agent since he opted out of his contract with the San Francisco 49ers in March. He filed a collective bargaining agreement grievance against NFL owners in mid-October, alleging they colluded against him for starting the trend of protesting during the national anthem last year.
"I am not going to stand up to show pride in a flag for a country that oppresses black people and people of color," he told Steve Wyche of NFL Media in August 2016. "To me, this is bigger than football and it would be selfish on my part to look the other way. There are bodies in the street and people getting paid leave and getting away with murder."
The 30-year-old made a $1 million pledge to help "organizations working in oppressed communities" as part of his effort to fight racial injustice.
"I plan to kneel until the president apologizes for the comments that he made, because I felt like those were very disrespectful comments that he made. The league is made up of, I think, ... over 70 percent African-Americans, so the people that would be kneeling for this cause would be African-Americans.
"To keep it honest, he was calling a lot of us, and I feel that he was calling myself, an S.O.B., and that's not OK and very disrespectful. So I plan to kneel until the president apologizes."
Meanwhile, Jim Trotter and Jason Reid of ESPN.com reported the NFL is trying to bring an end to protests during the anthem by making a proposal to the players that includes "at least $89 million over a seven-year period" to causes related to African-American communities. However, "not all players are in agreement" on the offer.