The Hammers will pay €12m (£10.1m) plus add-ons for the Germany international, per Sky Sports.
Kehrer has arrived in London for a medical and to finalise personal terms.
David Moyes is hoping to have Kehrer available for Thursday night's Europa Conference League qualifier against Danish club Viborg.
Kehrer is predominantly a centre-back but often features as a full-back for club and country.
The 25-year-old has won 20 caps for Die Mannschaft.