Rambis has already had a second interview with Minnesota, and the only step left is to talk with team owner Glen Taylor, who has said publicly he would be the final part in the decision-making process.
The longtime Laker has already met with new Timberwolves General Manager David Kahn. Rambis would get the nod for the position over two other candidates -- TV analyst Mark Jackson and Houston Rockets assistant coach Elston Turner.
Rambis has had a busy summer. He was a finalist to be the head coach for the Sacramento Kings and was also interviewed to possibly fill the head coaching vacancy with the Philadelphia 76ers. Sacramento hired Paul Westphal and Philadelphia hired Eddie Jordan.
Rambis had serious discussions with the Kings and was offered the job, but he wanted more than a two-year contract and more money than was offered.
With Minnesota, Rambis probably would get at least a three-year deal.
Rambis, 51, has been an assistant with the Lakers for 10 seasons and has filled in for Jackson for medical reasons on a number of occasions.
He was in charge of the Lakers' defense last season and was credited with the Lakers holding the Orlando Magic to only 91.2 points a game in the NBA Finals en route to winning the franchise's 15th championship.
Jackson gathered the Lakers coaches before training camp last October and told them he was appointing a defensive coach, something he hadn't done in his previous 17 years of coaching in the NBA.
"Kurt is real good at this and he's willing," Jackson said at the time.
Rambis would take over a Timberwolves team that finished 24-58 last season and fired Kevin McHale in June.
Rambis made a name for himself as a rough-hewn power forward for the Lakers during the Magic Johnson, Kareem Abdul-Jabbar Showtime era in the 1980s, providing muscle and energy under the basket for four of the Lakers' championship runs.
He played nine seasons for the Lakers.
Rambis was the Lakers' head coach in 1999, going 25-13 after taking over for Del Harris as interim coach.
Jackson was hired by the Lakers a few months later, ending Rambis' stint as head coach, though he eventually joined Jackson's staff.
In a touch of irony, Rambis would replace the man who clotheslined him on a vicious play during Game 4 of the 1984 NBA Finals, which were won by the Boston Celtics in seven games. McHale was the Celtics' star power forward at the time.
The Timberwolves have a very young nucleus, different from the veteran-laden team Rambis would be leaving.
Center Al Jefferson, 24, is expected to return for the Timberwolves after sustaining a torn knee ligament last February.