The word interesaríamos is the conditional form of interesar in the first person plural.
See the full interesar conjugation

interesar

¿Qué te hace pensar que nos interesaríamos?
What makes you think that we would be interested?
Normalmente no nos interesaríamos hasta que hubieran pasado un par de días.
Normally we wouldn't take an interest until we at least had a few days go by.
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