Jackson would receive $8.8 million under the franchise tag, which would nearly double his $4.5 million salary from last season. The window for teams to designate their franchise players begins Monday and ends March 5.
"We're looking for a long-term deal and that's what both parties would like to accomplish before free agency starts on March 13,'' agent Brian Mackler told the Plain Dealer.
Jackson, 28, is reportedly seeking a five-year deal. He led the Browns with a career-high 158 tackles, which ranked second in the NFL. His three defensive fumble recoveries tied for the most in the AFC.
This was a remarkable turnaround for Jackson, who had missed the previous 26 games with two separate pectoral injuries. He finished second to Detroit quarterback Matthew Stafford for NFL Comeback Player of the Year honors.
Jackson told the Boston Herald last month that he would be open to playing under the franchise tag.
"I want to be in Cleveland," Jackson said. "If it's the franchise tag, it's the franchise tag. As long as I still have my health, that's what is most important."
Jamison Hensley covers the AFC North for ESPN.com.