According to that: it is AM3 compatible, but only up to 95w processors, so the 965 is a no-go. A 95w Phenom II 945 should be okay though. If possible, a motherboard upgrade would be best, but ram and etc must also be upgraded.
The support list looks like it does not have any Zosma processors or maybe it was last updated before they were released. It should work, but you can't be sure it will be recognized unless there is a BIOS update available.
Wait, so in order for me to upgrade my processor I need to update the bios?