All perfect praise be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
It is prohibited for a person to touch the Quran when not in a state of Wudoo`, because Allah, The Almighty, Said: "which none touch except the purified," {Al-Waqi`ah, 79}.
Although the companions said that "the purified" refers to the angels, the word itself reflects the respect and veneration due to the Quran. Therefore, none may touch it save the purified. Another evidence on this is the Hadith: "Yahya related to me from Malik from Abdullah ibn Abi Bakr ibn Hazm that in a letter that the Messenger of Allah, may Allah bless him and grant him peace, sent to Amr ibn Hazm it said that no-one should touch the Qur'an unless he was pure." {Muwatta Malik}. This prohibition includes the pages of the Quran and, according to the stronger opinion of the Shafie scholars, the cover as well, since the latter is an integral part of it.
As for turning the pages of the Quran with a tool, such as a ruler or a pen, without needing to touch it, that is permissible. However, holding it using a piece of cloth or a sack and the like is impermissible, even if that didn`t involve touching it. This is because holding the Quran is greater than touching it. An exception to the aforementioned ruling is the situation in which the person, who isn`t in a state of Wudoo`, feared that the Quran could get torn or degraded.
Al-Khateeb Ash-Shirbini {May Allah have mercy on him} said: "It is permissible for the person , who isn`t in a state of Wudoo`, to hold the Quran for a necessity: fearing that it could drown, burn, be covered with impurities or fall in the hands of a disbeliever. In the latter situation, he`s obliged to save it." {Moghni Al-Mohtajj, vol.1/pp.150}. And Allah Knows Best.