It was the first meeting between the 49ers' embattled quarterback, Shanahan and Lynch since the latter two joined the organization during the offseason.
"I would characterize it as just a really positive discussion," Lynch said in a radio interview with KNBR, adding that he and Shanahan committed to being completely honest with Kaepernick.
Kaepernick, 29, can opt out of the final year of his contract and become a free agent next week.
"And I think as Kyle and I believe, the evaluation process is still very much fluid," Lynch told KNBR. "We've only been on the job a couple of weeks, and I can tell you we both very much enjoyed being around Colin, and he seems like he's in a real good place."
Kaepernick drew a national spotlight early last season for kneeling during the national anthem. He started the campaign as the 49ers' backup behind Blaine Gabbert before taking over as the starter on Oct. 16 against the Buffalo Bills.
With Kaepernick under center, the 49ers lost nine straight and 10 of 11 overall to finish the season with the second-worst record in the NFL at 2-14.
Kaepernick threw for 2,241 yards, 16 touchdowns and four interceptions while fumbling a career-worst seven times.
San Francisco also announced Wednesday that assistant general manager Tom Gamble is leaving the organization.
Gamble has 29 years of NFL experience, including 10 with the 49ers.
"The 49ers organization has tremendous respect and appreciation for Tom Gamble and his many years of service," Lynch said in a statement. "He is a class act who has helped a great deal in this transition, and I thoroughly enjoyed getting to know him.
"After working together over the last month, Tom and I agreed that it would be in both of our best interests for him to pursue other opportunities. Tom is a true professional and we wish him and his family great success in the future."
Gamble originally joined the 49ers in 2005 and served eight seasons in the personnel department, including two as the team's director of player personnel. He left to join the Philadelphia Eagles as the vice president of player personnel in 2013-14 before re-joining the 49ers in January 2015 as a senior personnel executive.
He was promoted to assistant general manager on July 25, 2016, under Trent Baalke, who was fired along with coach Chip Kelly in January.
"I must thank Jed, the York family and the entire 49ers organization for the wonderful memories they provided me and my family, but it is time I move on," Gamble said.