No. Animals can not become Buddha.
Even if an elephant or any other animal regulates his life right ,he will not attain insight into the Truth.
To quote from Questions of King Milinda:
'Venerable Nâgasena, those who regulate their lives aright--do they
all attain to insight into the Truth, or are there some of them who do
not?' 'Some do, O king, and some do not.' 'Then which do, Sir, and
which do not?' 'He who is born as an animal, O king, even though he
regulate his life aright, will not attain to insight into the Truth,
nor he who is born in the Preta world, nor he who holds wrong views,
nor the deceitful man, nor he who has slain his mother, or his father,
or an Arahat, nor he who has raised up a schism in the Order, nor he
who has shed a Buddha's blood, nor he who has furtively attached
himself to the Order , nor he who has become a pervert , nor he who
has violated a sister of the Order, nor he who, having been guilty of
one or other of the thirteen grievous offences , has not been
rehabilitated, nor a eunuch, nor an hermaphrodite--and whosoever is a
human child under seven years of age, even though he regulate his life
aright, will not attain to insight into the Truth. To these sixteen
individuals there is no attainment of insight, O king, even though
they regulate their life aright.'