The Detroit News reported contract details are still be worked on but an official hiring could be announced as soon as Wednesday.
Nelson, who spent most of this past season as interim head coach of the Edmonton Oilers, was an assistant with the Griffins in the 2002-03 season after playing parts of four seasons on their blue-line in the late 1990s and early 2000s when Grand Rapids competed in the old International Hockey League.
The 46-year-old would take over from Jeff Blashill, whom the parent Detroit Red Wings hired as head coach recently to take over from Mike Babcock, who left to coach the Toronto Maple Leafs.
Nelson replaced the fired Dallas Eakins in Edmonton, taking over on an interim basis alongside then-Oilers general manager Craig MacTavish. Having spent five seasons in the Oilers organization, he arrived from the team's AHL affiliate in Oklahoma City, where he turned around a minor league system and helped in the development of prospects Oscar Klefbom, Jeff Petry and Anton Lander.
Edmonton, with three wins in 27 games when Nelson arrived, had a 17-22-7 record the rest of the way.
But Nelson was out of work in mid-May when recently hired Oilers GM Peter Chiarelli brought former San Jose Sharks bench boss Todd McLellan to town.
In Grand Rapids, Nelson joins Griffins outfit that won the Calder Cup championship in 2013 and is fresh off a conference final appearance against Utica. While the team might lose top scorer Teemu Pulkkinen to the NHL, centre Dylan Larkin will return to the Griffins after leaving the University of Michigan following a standout freshman season.
Grand Rapids also boasts several skilled players in former Ontario Hockey League star Tyler Bertuzzi, Xavier Ouellet and Ryan Sproul. Rookie pro Anthony Mantha was called out by Red Wings management for a lack of production in the post-season but he was also coming off a broken leg. Recently, Mantha has been the subject of trade rumours.
A former assistant coach with the Atlanta Thrashers, Nelson left Grand Rapids in 2003 to coach the now-defunct United League's Muskegon Fury, winning back-to-back titles in 2004 and 2005. He was also on the bench as an assistant coach with the Chicago Wolves when they won the Calder Cup in 2008.