The Dolphins have been working on a long-term deal with Soliai, who at the very least will get a one-year contract worth roughly $12.5 million.
That would be a 25-fold increase over Soliai's $467,000 salary in 2010, when the 6-foot-4, 355-pound nose tackle emerged as a run-stopper after three disappointing seasons.
Soliai is expected to sign his tender by the end of the week, according to a league source.
Soliai's agent, David Canter, told the South Florida Sun-Sentinel earlier this week that Soliai wants a multiyear contract that exceeds the five-year, $20.5 million deal defensive lineman Randy Starks received in 2008.
"We want to be here. We've said it day in and day out. We want to be here," Canter said. "As long as everything works out and there's a new CBA, we can negotiate in good faith without the limitations of the 30 percent rule.
"We're going to give the Miami Dolphins as fair a shot as they would have ever hoped to get."