The two sides had been making progress on the deal as of Saturday before hitting a snag.
There has been plenty of speculation that Snyder would be dealt this offseason with the emergence of backup Miguel Montero last season. Snyder, who signed a three-year, $14.25 million extension last winter, was hampered for most of the 2009 season with back problems that eventually required surgery and limited him to just 61 games. He hit .200 with six homers and 22 RBIs.
Overbay was initially drafted by the D-backs in the 18th round of the 1999 First-Year Player Draft and played for the D-backs from 2001-2003 before being dealt to the Brewers prior to the 2004 season as part of a trade that brought Richie Sexson to Arizona.
Last season, the 32-year-old hit .265 with 16 homers and 64 RBIs in 132 games. Getting on base has always been a strength for Overbay, who had an on-base percentage of .372 in 2009. He is entering the final year of his contract and will make $7 million next year.
New Blue Jays GM Alex Anthopoulos has a policy of not commenting on rumors, but he did discuss trades in general terms on a conference call with Toronto reporters Saturday.
"I would say that I would probably be more active in trades than free agency," Anthopoulos said. "I think trades is definitely something that I'm going to be more aggressive with overall. That doesn't necessarily mean that they're going to occur, but it's probably a little bit more of a fit for our club right now."
D-backs GM Josh Byrnes, who also does not address trade rumors, declined to comment on Saturday.
Steve Gilbert is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.