Originally, every committed Muslim should try his best to steer clear of interest in all his dealings and daily activities. No one can say that paying the interest to construct the Mosque is unlawful but it is preferable to donate that which is purely halal to the Mosque.
as a workable solution, you should donate that interest money to any charitable organization which help champion the causes of the weak, poor or oppressed nations and the you can also get a righteous reward by donating from your purely halal money to help build the Mosque.
Dr. MonzerKahf, a Scholar in Islamic Economics & Financial Expert, states the following: Interest one earns does not belong to that person according to the Shari’ah. In principle, earned interest must be returned to its payer. If the payer is an interest practitioner such as a bank, you do not return it to the payer because doing so would amount to helping the bank to make more evil transactions. It also makes you appear as a fool and Muslims must not put themselves in a position to be fooled by anyone.
Consequently, the fatwa that is discussed and accepted by all contemporary Muslim scholars and that was adopted in the second conference of Shari’ah issues of Islamic banks held in Kuwait in 1994 suggests that we do not return earned interests to banks. This applies to the Muslims living in Muslim countries or in other countries. Such interest must be spent for the general welfare of Muslims and their communities.

As far as building masjids or Mosques is concerned, it is the obligation of Muslims. This means that they must pay for building masjids from their own money. While it is permissible to give interest to build masjids, this kind of action is not preferable because interest is dirty.
In fact, it is very often heard in the Shari’ah scholar circles; if you ever use interest in building Mosque facilities use it for the rest room structure not for the prayer hall structure.
I am personally of the view that we should give the earned interest to poor and needy Muslims or Muslims who are struggling to gain their political and territorial independence and leave the building of masjids from our own (clean) money. It is better to keep masjids clean of any haram money.
Based on the above, I suggest that you should give this money to the poor and the needy, general Islamic charitable causes and help those whose houses are being burnt in Palestine, Chechnya and India.