The 35-year-old, who previously spent five years with the Bluebirds, has been training with the club following his release by Palace at the end of last season.
"He's got to look at us and we've got to look at him," Solskjaer is quoted as saying by BBC Sport. "You never know in football. But at the moment it's just about training with us and keeping himself fit."
Gabbidon has been capped 42 times at international level for Wales.