Soliai will receive a one-year tender at $12.381 million -- the highest ever paid to a Miami defensive player. The contract would be guaranteed once he signs.
The 27-year-old Soliai had 39 tackles and two sacks for the Dolphins last season.
The 6-foot-4, 355-pound Soliai plays the nose tackle position in the Dolphins' 3-4 defense.
At the NFL scouting combine in Indianapolis on Thursday, Dolphins general manager Jeff Ireland said the Dolphins have been speaking with Soliai's representation about a contract extension and called it "a big need" to have Soliai on the roster.
ESPN.com NFL senior writer John Clayton and ESPN.com's Tim Graham contributed to this report.