No, because an animal companion wouldn't naturally get an opportunity to increase its Int score.
Animal companions don't get the "one every four HD" ability score bumps that a normal animal would. As their druid (or ranger) friend advances in level, the animal companion gains HD, as well as increases in Str and Dex, as illustrated in this chart from the "Animal Companion" section of the Druid class description:
Class Level Bonus HD Natural Armor Adj. Str/Dex Adj. Bonus Tricks Special
1st–2nd +0 +0 +0 1 Link, share spells
3rd–5th +2 +2 +1 2 Evasion
6th–8th +4 +4 +2 3 Devotion
9th–11th +6 +6 +3 4 Multiattack
12th–14th +8 +8 +4 5
15th–17th +10 +10 +5 6 Improved evasion
18th–20th +12 +12 +6 7
Later on, in that same section, it says:
"Bonus HD: Extra eight-sided (d8) Hit Dice, each of which gains a Constitution modifier, as normal. Remember that extra Hit Dice improve the animal companion’s base attack and base save bonuses. An animal companion’s base attack bonus is the same as that of a druid of a level equal to the animal’s HD. An animal companion has good Fortitude and Reflex saves (treat it as a character whose level equals the animal’s HD). An animal companion gains additional skill points and feats for bonus HD as normal for advancing a monster’s Hit Dice."
Note that that paragraph very specifically details what the animal companion gains as he gains additional HD, and ability score increases aren't among them.