AC Milan Noah Okafor (L) and Dortmund s German defender Nico Schlotterbeck vie for the ball during the UEFA Champions League match in Dortmund on Wednesday (AFP)
Both teams had plenty of chances but were unable to finish them off in an entertaining match.
Milan, which reached last season’s semifinals, also drew 0-0 at home against Newcastle in their Champions League opener. And it could be left counting the cost of its profligacy in both matches.
Newcastle surprisingly beat Paris Saint-Germain 4-1 to move top of Group F, a point above its opponent. Milan was two points behind Newcastle and one above Dortmund.
Dortmund was looking for its first points and first goal after losing its opener 2-0 at PSG.
The German side went close several times in the first half as Donyell Malen drilled just wide of the right post and Milan goalkeeper Mike Maignan pulled off saves to deny Niclas Füllkrug and Amir Bensebaïni.
Milan grew into the match and Giroud could have broken the deadlock in the 38th minute but he flicked the ball over the bar from six yards.
The Rossoneri had a triple chance on the stroke of halftime as Rafael Leão's cross from the left flank was pushed away from the onrushing Giroud by Dortmund goalkeeper Gregor Kobel. The move continued and Tommaso Pobega had a shot blocked before Theo Hernández fired the rebound over.
United States standout Christian Pulisic — who started his career at Dortmund — came close to marking his 50th Champions League appearance with a goal early in the second half but his effort was straight at Kobel.
Milan should have snatched all three points late on but Samuel Chukwueze and Tijjani Reijnders both fired narrowly wide.
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