The teams have had talks about a trade centered on Landry and Bears starting running back Jordan Howard, NBC Sports Chicago reported Saturday, citing sources.
Last week, Miami placed the franchise tag on Landry, who is balking at the idea of playing under those conditions and instead is seeking a long-term deal.
The website reported that the teams also would exchange first-round draft selections -- Chicago owns the No. 8 pick while Miami is at No. 11 -- and the Bears also would receive a third-round selection.
However, profootballtalk.com quoted a league source that said there was "no way" such a trade would be completed.
New Chicago coach Matt Nagy has been complimentary of Howard, who is the first player in franchise history to rush for at least 1,000 yards in each of his first two seasons.
However, Nagy's offense in Kansas City involved backs with pass-catching skills, not a strong suit of Howard, who had only 23 receptions last season.
Chicago is in desperate need of an upgrade at wide receiver. The 25-year-old Landry led the league in receptions (112) and amassed 987 yards and a career-high nine touchdowns last season. His 400 receptions are the most for any player in his first four NFL seasons.