To approach personally
appeal to, apply to, address, speak to, talk to, propose, request, accost, direct oneself to, make advances to, make overtures to, take aside, talk to in private, buttonhole*, corner*, descend on, descend upon*, sound out*.
Antonyms avoid*, shun, turn away.
To come near in space
near, come near, come nearer, go toward, move toward, drift toward, come up to, step up to, roll up to, advance, loom up, creep up, drive up, verge upon, draw near, go near, converge on, advance on, gain on, come into sight, progress, close in, surround, come forward, come closer, catch up to, overtake, bear down on, edge up to, ease up to, head into.
Antonyms leave*, recede, depart.
To come near in time
be imminent, be forthcoming, threaten, slip by, loom
(up), await, near, draw near, impend, diminish, decrease, grow
short, stare one in the face*, be around the corner*.
Antonyms recede, extend, stretch out.
To approximate
come close to, approximate, compare; see equal, resemble.