The short answer is: No, Mars has never and will never appear as large as the Moon.
The long answer is: Because Earth moves faster around the Sun than Mars does, our planet overtakes and passes Mars in its orbit. When Earth is roughly between the Sun and Mars, we say that Mars is at opposition (as in...Mars is positioned opposite the Sun in Earth's sky). This happens every 26 months.
Mars's orbit is fairly elliptical. At its closest point (perihelion), Mars is about 207 million kilometers from the Sun, and at its farthest point (aphelion), Mars is about 249 million kilometers from the Sun. When opposition occurs close to Mars's perihelion, which happens about every 15 or 17 years, then Mars might appear particularly bright in Earth's sky.
But even then, it will *never* appear as large as the full Moon. Even under the very best conditions, Mars is still 142 times farther away from Earth than the Moon is. And since Mars is only about twice as large as the Moon is, that means that at the very best, Mars is about 70 - 75 times smaller than the Moon.
On August 27, 2003, Mars's opposition coincided with Mars's perihelion, prompting a flurry of news stories. One astronomer said, correctly, that when viewed through a telescope magnified 75 times, Mars would look as big as the full moon looks to the naked eye. Some careless reporter left out the bit about the telescope, saying that Mars would look as big as the full moon...period. And thus, the Mars-Moon hoax was inadvertently born. Since then, a few weeks before August 27 *every year*, somebody starts passing around memes about Mars looking as big as the Moon. Lately, it seems they pass around the meme whenever they want to have a laugh at some foolish person's expense.
Here's the truth: Mars will never, ever, EVER look as large as Earth's moon in Earth's sky. Ever.
I hope that helps. Good luck!