sound out

sound out sb/sth AND sound sb out (about) (try to find out from sb what they think about sth, often in an indirect way; find out what someone’s opinion about something is) — расспрашивать (с целью прозондировать почву, выяснить косвенно то, что интересует); разузнавать; выспрашивать

Example 1: They decided to sound out her interest in the project.

Example 2: We should sound out the boss about getting a new coffee machine.

Example 3: I sounded her out about working for us but she wasn't interested. (CIDI)

Example 3: We need to sound out his views on the project before we go ahead (CIDI)

see also
[probe the ground]
[put out one's feelers]
[test the water]