If you want to sit in the mosque to listen to the khutbah, that is not permitted, because it is not permitted for a menstruating woman to enter the mosque, unless she is only passing through.
But if she is going to sit in a place that is attached to the mosque or close to it, then there is nothing wrong with that, because she is not entering the mosque in this case.
For a more detailed answer regarding places that are attached to the mosque, please see the answer to question no. 34815, to find out when the place attached to the mosque comes under the same ruling as the mosque itself.
Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) said:
It is haraam for a menstruating woman to stay in the mosque; it is even haraam for her to stay in the Eid prayer place, because of the hadeeth of Umm ‘Atiyah (may Allaah be pleased with her) who said: “He (meaning the Prophet (peace and blessings of Allaah be upon him)) commanded us to bring out on the two Eids the adolescent girls and the virgins in seclusion, but he commanded the menstruating women to stay away from the prayer-place of the Muslims.” Narrated by al-Bukhaari, 324; Muslim, 890. Risaalat al-Dima’ al-Tabee’iyyah li’l-Nisa’, p. 52-53.
The Standing Committee (5/398) was asked about the ruling on menstruating women entering the mosque.
They replied: It is not permissible for a menstruating woman to enter the mosque except to pass through it if she needs to. This is like the one who is junub (in a state of impurity following sexual activity), because Allaah says (interpretation of the meaning):
“O you who believe! Approach not As-Salaah (the prayer) when you are in a drunken state until you know (the meaning) of what you utter, nor when you are in a state of Janaaba (i.e. in a state of sexual impurity and have not yet taken a bath), except when travelling on the road (without enough water, or just passing through a mosque), till you wash your whole body”
The Standing Committee was also asked (6/272) about the Islamic ruling on a woman who enters the mosque when she is menstruating so that she can listen to the khutbah.
They replied: it is not permissible for a woman to enter the mosque when she is menstruating or bleeding following childbirth… But simply passing through is allowed, if she needs to and she is certain that she will not make the mosque naajis (impure, i.e. by drops of blood falling on the floor), because Allaah says (interpretation of the meaning):
“…nor when you are in a state of Janaaba (i.e. in a state of sexual impurity and have not yet taken a bath), except when travelling on the road (without enough water, or just passing through a mosque)…”
A menstruating woman comes under the same rulings as one who is junub, because the Prophet (peace and blessings of Allaah be upon him) commanded ‘Aa’ishah to pass him something from the mosque when she was menstruating.
And Allaah knows best.