The 37-year-old player has struggled for game time this season having made 11 appearances in the Premier Soccer League (PSL).
Gould, who joined the PSL debutants after leaving SuperSport United last year, has three months left in his contract with Stellies.
Barker wants the experienced player to stay with the Western Cape-based side as he has been helping the youngsters in the team.
“When we come back (from the suspension of games due to coronavirus) we will sit down with him and discuss the whole season,” Barker told Isolezwe.
“It is true that he does not play often, but he has helped a lot of young players and he has played very well in the games he has played.”
Central defenders Robyn Johannes and Sibusiso Mthethwa have been preferred ahead of the former Kaizer Chiefs centre-back this season.
“There is a lot to look at, but I believe he still needs to be in the team,” the former University of Pretoria coach added.
“Personally, I want to keep him for next season. But this will be determined at the end of the season. ”
Stellenbosch are placed 11th on the league standings – four points above the relegation play-off spot and four points behind eighth-placed Highlands Park.
The PSL has been suspended until further notice in response to the coronavirus outbreak in South Africa.