Jackson was made a free agent by the St Louis Rams after last season, ending a highly-successful nine-year stint with the franchise during which he became their leading rusher of all time with 10,135 yards.
The 30-year-old composed a list of what he wanted from any interested teams and insists that he would have retired from the sport had his criteria not been met.
"It was a real, legitimate option for me," ESPN quotes Jackson as saying.
"It probably wouldn't have been fun now, this time of the year because I know I have a lot left in the tank, but I am one of those hard-headed guys. Once I believe in something, I stick to it."
Jackson will face his former side for the first time since leaving when the Falcons take on the Rams on Sunday.