Howard told reporters he hasn't signed the legal document yet because there is some "little stuff" to work out, but he is hoping to sign by the weekend.
TSN reports the deal is worth $31.8 million.
"I wanted to be here," Howard said. "I get along great with everyone here. I believe in this organization. I just want to be here and get the job done."
Howard was an all-star last season and has won at least 35 games in three straight seasons. He is 16-12-4 with a 2.41 goals-against average and .917 save percentage this season.
He was a second-round draft pick for the Red Wings in 2003 and spent four seasons in the American Hockey League with the Grand Rapids Griffins after playing three seasons at the University of Maine.
"Obviously he's always worked hard and the organization has confidence in him," Red Wings coach Mike Babcock said. "It's important for us. We need good goaltending. We need him each and every night and he's been excellent for us."