You want to say that in the past you formed an intention to call Jane, and that intention has persisted into the present because it has never been fulfilled. Look at your options for expressing this:

SIMPLE FORMS

I mean to call Jane.
This form describes your present intention. It says nothing about the past.

I meant to call Jane.
This form describes a completed past intention—the technical term is perfective, which is quite different from "perfect" constructions. It implies that the intention was either fulfilled or dropped. It says nothing about the present.

PROGRESSIVE FORMS

^✲I am meaning to call Jane.
^✲I was meaning to call Jane.
These forms are prohibited in ordinary use, because mean to is a stative verb like know, have, live, and these verbs have the progressive sense "built in". The prohibition is weaker in the past form, which may be employed to specifically exclude the perfective sense: I was meaning to call Jane, but kept forgetting. You'll occasionally find this in colloquial use instead of the perfect progressive: I was meaning to call you.

PERFECT FORMS

I have meant to call Jane.
I had meant to call Jane.
These forms describe an intention held before a present (have) or past (had) Reference Time (RT) which led to some sort of a state which obtains at RT. With mean to it is ordinarily used to cast light on a current situation by pointing to past intention, so it tends to be restricted to formal "forensic" discourse: I have meant to assail the motives of no party, or individual; and if I have, in any instance (of which I am not conscious), departed from my purpose, I regret it. — A. Lincoln.  You could use this in the present context, but the intention would be seen retrospectively, and the second clause should be recast to suit it: "I have meant to call Jane, but have repeatedly forgotten to." It would neither imply nor exclude the persistence of your intention into the present.

PERFECT PROGRESSIVE FORMS

I have been meaning to call Jane.
I had been meaning to call Jane.
These are the forms ordinarily employed in both formal and informal registers to express an intention formed before the (present or past) RT and persisting into RT. The perfect piece of the construction (have/had) expresses the existence of the intention before RT, and the progressive piece (BE -ing) expresses persistence, excluding perfectivity.

Incidentally, mean to (as opposed to bare mean) is one of a class of verbs which act as semi-auxiliaries—the to means that they take a to-infinitive.

get to
happen to
have to
seem to
tend to
turn out to
used to
be about to
be going to
be likely to
be supposed to

Each of these follows its own set of 'rules', depending on its semantic character.