Yes, it was a quote of Jesus, although a misquote.
It can be found in Matthew 9:17 (the first book of the New Testament)
When the religious authorities were trying to criticize Jesus and his disciples, as well as Jesus' teachings, saying they went against the old testament laws and traditions, Jesus was saying that what he was offering was fresh and new, and just didn't fit their old ways of thinking which had lost God's intended focus. Old wineskins were brittle, inflexible. New wine was fermenting, giving off gas. You needed newer flexible wineskins to expand and stretch as the young wine still gave of CO2, or else, new wine in old wineskins would burst the dry skins, losing everything. So too, God's purpose in Jesus needed open, hungry and humble hearts to be received, instead of inflexible, immoveable traditions and attitudes.
Hope that's helpful.
Rick Fremont, MI