The two sides have agreed on the terms of the deal, but still are signing off on the language of it. The deal will not be signed until the language is completed.
The numbers were projected to come in north of $12 million a year, which means the deal will be worth more than $60 million dollars. Suh is guaranteed $40 million.
Lions spokesman Bill Keenist said the team had nothing to announce or confirm at this time.
Suh was scheduled to fly from Nebraska to Michigan on Wednesday morning to sign his contract and practice with the Lions during the afternoon, a person familiar with his itinerary told The Associated Press. The person spoke on the condition of anonymity because both sides were not publicly discussing Suh's plans.
The second overall pick in April's draft missed four days of practice, including the team's first workout in full pads on Tuesday morning.
"We have six days in shoulder pads and we have six full-padded practices in training camp. And we've already finished two of those shoulder-pads practices," Lions coach Jim Schwartz said on Monday. "Those are opportunities that, once they're gone, they're gone forever. You're not getting them back. ... That's the disappointing thing from his standpoint. That's work that you can't get back there."
Veteran center Dominic Raiola also seemed anxious for his teammate to get to camp.
"I haven't even sent him a text or anything, but I'd like to tell him, 'Just sign the damn contract already. You are missing some good things here,'" Raiola said, according to the Detroit News.
Detroit hoped the former Nebraska star could bolster a defense that has ranked among the league's all-time worst in points allowed the past two seasons. The Lions won two games last year after becoming the first team in league history to go 0-16.
The 6-foot-4, 307-pound Suh was the first defensive player to win The Associated Press College Football Player of the Year award since its inception in 1998. He had 4½ sacks against Texas in the Big 12 title game and finished the season with 12.
Suh, a Heisman Trophy finalist, was the first defensive tackle to be drafted among the top two picks since Oakland took Darrell Russell in 1997.
His mother, Bernadette, is a schoolteacher from Jamaica who required her son to post a 3.0 grade-point average before he could play football. His father, Michael, was born in Cameroon and became a mechanical engineer after moving to Portland, Ore.
Suh graduated from Nebraska with a degree in construction management from the College of Engineering. He announced in April he will donate $2 million to the school's strength and conditioning center, and an additional $600,000 for an endowed scholarship in the university's College of Engineering.
The Lions have had only one player, Calvin Johnson, miss more than a couple days since Bryant Westbrook was a long-term holdout in 1997. Westbrook's agents were Roosevelt Barnes and Eugene Parker, both of whom are representing Suh.
Suh posted a message on his Twitter account Sunday that quoted a biblical passage: "Judge not by with appearances, but judge with the right judgment."
Adam Schefter is an NFL reporter for ESPN Insider. Information from The Associated Press contributed to this report.