"It is a tough situation," the insider added, responding to British reports of the union's demise. "[I] don't think that anyone who knows them and cares about them doesn't have an opinion about why they should [split], but it's not happening now."
According to the source, Winehouse's "health and wellbeing" remain the most immediate concerns for those close to her.
The 24-year-old singer spent Friday night at London's Holborn police station after being found unfit for questioning. She was released Saturday morning after having been arrested and issued a formal caution for common assault.
On Sunday, Winehouse's father Mitch told the U.K.'s News of the World that he wanted the Grammy-winner locked up in a mental hospital for her own protection.
"I want her sectioned," he said. "The situation is getting out of control. I want her off the street."
Winehouse met Fielder-Civil, a part-time gofer on video sets, at a London bar in 2003. The on-again, off-again couple got hitched in Miami in May 2007.