The Warlock class feature, "Pact of the Blade" gives you two options to make a pact weapon:
Option 1: Creating a pact weapon
If you create a pact weapon, you can choose it's form, but are limited to melee weapons listed on the "Weapons" table in the player's handbook:
Rules answers, April 2016:
The warlock’s Pact of the Blade feature (PH, 107–8) lets you create a melee weapon out of nothing. Whenever you do so, you determine the weapon’s form, choosing from the melee weapon options in the Weapons table in the Player’s Handbook (p. 149).
So, you could select quarterstaff. But just because an arcane or druidic focus staff can act as a quarterstaff, that doesn't necessarily mean that a quarterstaff can act as a focus staff. Neither the arcane staff nor druidic staff are ordinary quarterstaffs.
Arcane staff, PHB p. 151:
a specially constructed staff ... designed to channel the power of arcane spells.
Druidic staff, PHB p. 151:
... a staff drawn whole out of a living tree ...
A created pact weapon certainly isn't drawn whole out of a living tree, and nothing in the rules indicates that it is designed to channel the power of arcane spells.
Option 2: Transforming a Magic Weapon
While, I am not aware of any magic weapon that explicitly acts as a arcane or druidic focus, Jeremy Crawford has given his opinion on twitter, that any magic wand can be used as an arcane focus. So your DM may take that into consideration, and also agree that any magic staff can also act as an arcane or druidic focus.
Also, there is nothing preventing your DM from putting such an item in your game, and per the rules you would be able to make it your pact weapon. As far as I can tell, this is your only option.