Yes and no. No, there is not and never has been any romantic liaison between them. But it's fair enough to assume they are good friends who. Of the relationship between Gandalf and Galadriel, If Gandalf was Olorin then he spent countless ye. Indeed, Galadriel had wanted Gandalf to be head of the council (much to Middle Earth (excluding the other Istari) the Lady Galadriel had lived in the West and.
The two "shared the joys and burdens of bearing two of the Elvenrings". They would most certainly have been aware of the other bearer, whether this had an affect on their relationship isn't certain. She strongly supported Gandalf's case to be the head of the White Council, putting him against Saruman, the eventual leader. Galadriel indeed had wished that Mithrandir should be the head of the Council, and Saruman begrudged them that, for his pride and desire of mastery was grown great; but Mithrandir refused the office, since he would have no ties and no allegiance, save to those who sent him, and he would abide in no place nor be subject to any summons.
Liberties of such are taken in the Hobbit films, but even in the books we see Galadriel seemingly reading people's mind, and she was able to "sense" Gandalf's death against the Balrog and sent Gwaihir to his aid, and clothed him in white with a new staff.
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Healing I found, and I was clothed in white. The Two Towers The loss of Gandalf seems to take a significant toll on the Lady Galadriel, saying she could no longer see him nor the paths upon which he walks. The Mirror of Galadriel While reading through The Mirror of Galadriel for this answer I'd noticed something else, Galadriel is quick to defend Mithrandir when her husband, Celeborn, calls him foolish.
And if it were possible, one would say that at the last Gandalf fell from wisdom into folly, going needlessly into the net of Moria. Those that followed him knew not his mind and cannot report his full purpose. But however it may be with the guide, the followers are blameless. Do not repent of your welcome to the Dwarf. However, during the Third Agewhen the One Ring was lost, she put it to good use protecting the borders of her realm, for the powers of her ring were protection, preservation, and concealment from evil.
The tales tell little of Galadriel or of Celeborn during many centuries in the Third Age, but after the formation of the White Council in TA she put forth her might in opposition of Sauron. She played a pivotal role in the formation of the Council, though her counsel to put Gandalf at its head was not followed.
War of the Ring Galadriel pours water into her Mirror. Once in Caras GaladhonGaladriel allowed Frodo and Sam to peer into the Mirror of Galadrielenabling them to glimpse possible events of the future. She, in turn, was tested when Frodo Baggins later offered to place the One Ring in her keeping.
Question: Did Mithrandir (Gandalf) and Galadriel have a relationship at one point?
To illustrate what would happen if she accepted, she presented an image of herself corrupted by the ring, declaring, "In place of the Dark Lord you will set up a Queen. And I shall not be dark, but beautiful and terrible as the Morning and the Night! Fair as the Sea and the Sun and the Snow upon the Mountain!
Dreadful as the Storm and the Lightning! Stronger than the foundations of the earth. All shall love me and despair! Not dark, but beautiful and terrible as the dawn! Treacherous as the sea! Stronger than the foundations of the earth! All shall love me, and despair!
As the Fellowship departed, she gave each member a gift and an Elven cloak, and outfitted the party with boats and supplies. Gimli, in particular, was touched by Galadriel's lordliness and beauty, and asks for one strand of her golden hair as an heirloom of his house; she generously gave him three, which he later set in an impregnable crystal. Apart from the strands of hair given to Gimli, she gave a Mallorn seed and a small box of earth from her garden to Samwise Gamgee ; a green stone set in silver to Aragornalong with a scabbard for his sword; and a belt each to BoromirMerryand Pippin.
In place of the Dark Lord you will set up a Queen. And I shall not be dark, but beautiful and terrible as the Morning and the Night! Fair as the Sea and the Sun and the Snow upon the Mountain! Dreadful as the Storm and the Lightning! Stronger than the foundations of the earth. All shall love me and despair! Then she let her hand fall, and the light faded, and suddenly she laughed again, and lo!
When she met the Fellowship in her tree-dwelling in Caras Galadhonshe gave each member a searching look, testing their resolve—though Boromir interpreted this test as a temptation. She was in turn tested when Frodo Baggins offered to place the Ring in her keeping. Knowing that its corrupting influence would make her "great and terrible", and recalling the ambitions that had once brought her to Middle-earth, she refused the Ring.
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She accepted that her own ring's power would fail and that her people would diminish and fade with the One Ring's destruction, and that her only escape from the fading of the Elves and the dominion of Men was to return at last to Valinor. There is the suggestion in the novel, backed up by other writings,  that in acknowledgement of this renunciation of power her personal ban from Valinor was lifted and she was finally given leave to return over the sea.
Her husband Celeborn likewise provided the Fellowship with Elven-boats. Galadriel healed his wounds and reclothed him in white, signaling his new status as head of the Istari.
Celeborn remained behind, and Tolkien writes that "there is no record of the day when at last he sought the Grey Havens". She was well overyears old at that time.