According to the player's manual, a character with intelligence = 10 who wants to make a multiclass wizard needs to have a minimum of intelligence = 13. If in the course of an adventure you find an object that increases your intelligence to 19 while it is equipped, does it meet the requirements or are the requirements supposed to be without magic or alterations, minimum characteristic base? In chapter 6 of the player's manual that possibility is not mentioned or I have not found it.
Said magic item would raise your effective Intelligence score, but not your actual score, so this would not allow you to multiclass. Only an item like the Tome of Clear Thought, which states "...your Intelligence score increases..." would affect your actual score.
However, while worn, you would get the benefits of the higher Intelligence score (saves, ability checks. etc.).