No, staves can be neither enchanted nor disenchanted.
If you're on PC, you can use the Creation Kit to either create a new staff or customize an existing one (Unique staves are good candidates, as modifying them will not change the ones NPCs will use against you).
With Dragonborn, you can craft staves, but they are the same staves you could find or buy elsewhere - you cannot create custom staves.
At the moment, no mods appear to have been developed that add this functionality.
gaming.stackexchange.com/users/19827/kotekzot
You can make some conjuration staffs at the Atronach Forge, but there's no in-game ability to do much beyond that.
As others have said, there's no way to disenchant staffs or make staffs with custom enchantments.
http://www.uesp.net/wiki/Skyrim:Atronach_Forge
gaming.stackexchange.com/users/6274/Iszi
No.
I'm sure there are several mods by now that allow this, but in the base game, there is no way to create your own stave.
gaming.stackexchange.com/users/3129/LessPop_MoreFizz
There are some unenchanted staffs in the qasmoke editor's test cell, but you need to be on pc
gaming.stackexchange.com/users/23310/moopman9000
In the Dragonborn DLC, By completing the "Reluctant Stewerd" quest for Neloth in Tel Mithryn you gain the key to access his Staff Enchanter.
Which uses Heart Stones in Combination with the spell itself and an Un-Enchanted Staff which comes in various types, e.g. Un-Enchanted Alteration Staff.
All Un-Enchanted Staffs can be purchased from Neloth.
Just to Be clear, you can't enchant staffs without the DLC
gaming.stackexchange.com/users/67678/CerberusN61
I´ve been willing to create a mage character, since there are some good looking staves in the game.  But, there is there any way to disenchant those staves ? If yes, is there any non enchanted staff in the game so i can enchant with my own enchantings ?
Is there any non-enchanted Staff in Skyrim?
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gaming.stackexchange.com/questions/51160
gaming.stackexchange.com/users/15626/Marcello Grechi Lins
There is no way to disenchant staffs. You can use Creation Kit to create a new staff or customize an existing one. While it is not possible to create staffs that bare any enchant, there is a limited freedom to craft some either by exploiting the game or by progressing through the DLCs.
It seems that it is impossible to craft custom staffs. It is suggested that there are ways to create few staffs.