Cloutier, 33, who contacted the club and asked for the tryout, hasn't played since appearing in nine games with the Los Angeles Kings in 2007-08. He has been bothered by a series of ailments, including a season-ending hip injury midway through 2006-07.
A 10-year NHL veteran who also has played for the Rangers, Tampa Bay and Vancouver, Cloutier is best remembered -- by Detroit fans -- for letting in Nicklas Lidstrom's shot from center ice in Game 3 of the 2002 first-round playoff series against the Canucks.
The Red Wings, reeling after losing the first two games of the series at home, went on to win the Stanley Cup.
Cloutier has a career NHL record of 139-142-33, with a 2.77 goals-against average and .899 save percentage.