1. To present (itself) as a possibility or (usually desirable) opportunity in the near future, especially temporarily. It was hard leaving my parents and all my friends from high school, but when an opportunity to attend school in Europe knocked on the door, I knew I had to seize the chance. What would you do if the chance to make half a million dollars was suddenly knocking on the door?

2. To try to become involved in some group or venture. If that kid is knocking on the door, you better let him join the team—he's really talented.

3. To be close to overtaking a competitor. Philly still sits atop the division, but Boston is knocking on the door with this win streak.