David Benner discusses in "Spirituality and the Awakening Self" (2012) a knowledge of God that is "transrational" and "contemplative" in chapter 5: "Learning from the Christian Mystics."
Christian mysticism should . . . not be confused with experience. Instead, it should be understood as participation in the mystery of the transformational journey toward union with God in love. . . . Mystics are . . . much more defined by their longing than by their experience. They long to know God's love and thereby to be filled with the very fullness of God [Eph 3:17-19].
This sort of knowing is beyond reason, but it is not irrational. It is transrational. It is knowing of a different order. It is a form of knowing often described as contemplative. And this is the connection to mysticism. Contemplation is apprehension uncluttered by thought—particularly preconception and analysis. It is based on direct and personal encounter.
When you know something by means of such encounter, you may not be able to express it verbally, at least not in a compelling, coherent, or exhaustive manner. But you do know that you know because your knowing has a depth and immediacy to it that is never present in simply knowing about things—even merely knowing about God. [pp. 75-76]