The two clubs were paired together in the group stages, with the Spanish side only managing a draw at home to the Rossoneri before defeating the Italians 3-2 in an epic at San Siro
The Blaugrana have already faced the Rossoneri twice in this season's competition, having been placed in the same group as the Italian champions.
Barcelona got the better of Milan by managing to triumph 3-2 at San Siro after being held to a 2-2 draw at Camp Nou, but they were made to work hard for their four points and for that reason, Guardiola is keen to steer clear of Massimiliano Allegri's side for at least one more round.
"I would like to avoid Milan in the quarter-finals," the former Spain international told reporters ahead of Friday's draw.
"We have already played [twice] and they are one of the biggest clubs in Europe.
"However, to reach the final in Munich, there is still so much to accomplish and above all, there remains the need to clash with the best."
Barcelona booked their place in the last eight with a 10-2 demolition of Bayer Leverkusen on aggregate, while Milan scraped past Arsenal by one goal, after beating the English side 4-0 at the San Siro and losing 3-0 in the away leg.
Want to be at the Euro 2012 opener? Who doesn't? With Sharp FanLabs you can win free tickets to the opening event of 2012's biggest tournament. Click here to take part!