Idiom
leave open the possibility of doing somethingleave open the possibility of (something/doing something)
to not prevent something from happening.The spokesman left open the possibility of another meeting before the Israeli leader left Washington.
Usage notes: also used with that:
His retirement leaves open the possibility that a new judge will be appointed this year.
followed by "of" in nearly 50% of cites, more than anything else; also exists as "hold/keep" open the possibility, but freq are 0.8/0.3 respectively--SL, 1/03
Related vocabulary: leave something open