  We aim to classify codimension 1 foliations $\mathscr{F}$ with canonical
singularities and $\nu(K_{\mathscr{F}}) < 3$ on threefolds of general type. We
prove a classification result for foliations satisfying these conditions and
having non-trivial algebraic part. We also describe purely transcendental
foliations $\mathscr{F}$ with the canonical class $K_{\mathscr{F}}$ being not
big on manifolds of general type in any dimension, assuming that $\mathscr{F}$
is non-singular in codimension $2$.
