Stoughton says the reason for the move will remain within the team that Gould helped win world championships in 1996 and 2011.
"There's multiple reasons why we could keep a player or release a player,'' Stoughton said Monday. "All of those things have been discussed within the team and they're going to stay within the team.''
Gould, who runs a roofing company in Winnipeg, could not be reached for comment.
The Stoughton rink failed to make it to the Brier this year, losing the three-versus-four game in the provincial tournament to Brandon's Rob Fowler, who curled with Stoughton from 2006 to 2010.
"We didn't play our best that week," said Stoughton. "We didn't deserve to go (to the Brier)."
Fowler went on to beat top-ranked Mike McEwan in the final to represent his province for the first time as a skip at the Brier. He curled there as a member Stoughton's team in 2007 and 2010.
Stoughton said a replacement for Gould has yet to be found but the team might try someone out during its final two cashspiels of the season.
"It might be a good opportunity to bring in a player," he said.
The Victoria Curling Classic (Mar. 29) and GP Car and Home Players Championship in Summerside, P.E.I. (April 17) are the last major events on the pro circuit this season.
Another prominent Manitoba curler and former world champion, Jennifer Jones, took a lot of flack two years ago when she sacked longtime third Cathy Overton-Clapham.
She is still criticized for the decision.
"It's one of the toughest decisions to make and hopefully we've made the right decision and our team can move forward and so can Steve," said Stoughton. "We thought we might be able to get better and that's your bottom line and it may work or it may not."
Stoughton's long-range target remains representing Canada at the 2014 Olympics in Russia.
"Our main goal is to first get into those (Olympic) curling trials in 2013 here in Winnipeg," he said.
Stoughton has failed in his two previous attempts to qualify for the Olympics, finishing second in 2005 and third in 2009.
Stoughton has won three Briers — 1996, 1999 and 2011. Gould wasn't with him in 1999 and Stoughton lost the final at the world championship to Hammy McMillan of Scotland.