In late 2009, Animaniacs co-creator Tom Ruegger wrote:

Quote Originally Posted by Tom Ruegger
Martianinvader wrote: "I've also heard this rumor: Fox wanted to keep Animaniacs, but they were going to pull the weekday run and only air it on weekends with sparse new episodes, like they did to Batman. So WB said no."

Never heard that. I doubt it. Sort of a moot point.
I found the source of the former statement. It was in an interview with the first president of Fox Kids, Margaret Loesch. The article is titled "Champions Series: A salute to Margaret Loesch: In her own words". It was published on November 1, 1996.

Quote Originally Posted by Margaret Loesch
At the time we made the Warner Bros. deal, we hadnít anticipated a hit like Power Rangers, and when it came time to renew our rights to Animaniacs, I didnít have a Monday through Friday time period for it. I couldnít very well pull Power Rangers, the number one show for kids in America. So I tried to work out an arrangement with Warner Bros. We offered to keep Animaniacs and put it on Saturday morning for an hour for one year and the following year, when other commitments were out of the way, put it back Monday through Friday. Much to my dismay and disappointment, Warner Bros. chose not to accept the alternative offer.
These are more press quotes about the Fox/WB dispute. The first quote is by Mediaweek writer Eric Schmuckle. It was in an article titled "The new face in toontown" that was published on April 17, 1995.

Quote Originally Posted by Eric Schmuckle
Fox and Warner tussled a year ago over Fox's option on Animaniacs. Fox couldn't find room on its weekday schedule for the show because of other commitments, so the show will become WB's flagship after this season. Last month, Fox moved the Saturday edition of Animaniacs to the low-rated 8 a.m. slot. MacCurdy believes Fox wouldn't have done that if it had the show next season.
This quote is by Los Angeles Times writer N.F. Mendoza. It was in an article titled "WB Raises the Animation Ante" that was published on October 22, 1995.

Quote Originally Posted by N.F. Mendoza
Since its 1993 premiere, "Animaniacs" aired on Fox--then it slipped through the cracks.

"Fox had an option they couldn't deliver on," explains Kellner, president of Fox Broadcasting from its 1986 start until he joined WB. "Fox made too many commitments to too many buyers and ran out of time periods."

Basically, Kellner says, part of Fox's contractual agreement with Warners was that "Animaniacs" run in a certain time slot. Apparently Fox promised that slot to someone else, he says. Warners exercised its option and took back its popular show. "I think it was an error they not maintain that prime position," Kellner says.
If you read between the lines, the show that replaced Animaniacs on weekdays was X-Men.

This was Fox Kids' afternoon schedule in the 1994-1995 season:
Tiny Toon Adventures
Taz-Mania
Animaniacs
Mighty Morphin Power Rangers

This was Fox Kids' Fall 1995 afternoon schedule:
Taz-Mania
X-Men
The Adventures of Batman & Robin
Mighty Morphin Power Rangers (Mon-Thu) / Goosebumps (Friday)

Ironically, X-Men was not a success on weekdays. In early 1996, Fox replaced it with Eek!Stravaganza. However, X-Men continued to air on Saturday mornings until January 24, 1998.