The 25-year-old has been identified by the Hammers as a top target following the sale of Issa Diop to Fulham as well as the injury sustained to summer signing Nayef Aguerd during pre-season.
The latter recently underwent surgery after tearing ankle ligaments in a friendly defeat against Rangers in July, and the 26-year-old could now face up to three months on the sidelines.
West Ham have since held talks with PSG over a deal for Kehrer and Sky Sports News reports that a fee of €12m (£10.1m) plus add-ons has been agreed between both parties.
Kehrer has landed in London for his medical and is understood to have already agreed personal terms on a five-year contract.
West Ham are hoping to complete the deal in time for the defender to be available for the first leg of their Europa Conference League playoff against Viborg FF on Thursday.
The report adds that Sevilla were also interested in the Germany international, but the Hammers have won the race for his signature.
Kehrer, who has less than 12 months remaining on his contract at the Parc des Princes, has fallen down the pecking order at PSG, with Marquinhos, Presnel Kimpembe, Sergio Ramos all preferred ahead of him by new manager Christophe Galtier.
The former Schalke man, who can operate at either centre-back or right-back, has not been involved in any of PSG's opening three games of the new season amid uncertainty over his future.
Kehrer is now set to end his four-year spell in the French capital, where he made 128 appearances across all competitions and won a total of eight trophies.
The arrival of Kehrer at West Ham will see the club's summer spending exceed £100m, having already recruiting Aguerd, Alphonse Areola, Flynn Downes, Gianluca Scamacca and Maxwel Cornet earlier in the window.
David Moyes's side remain active in the market, however, and they are allegedly targeting moves for Chelsea left-back Emerson Palmieri and Club Brugge midfielder Hans Vanaken.
West Ham are currently in advanced talks with Chelsea over a £13m deal for 28-year-old Emerson, who is now behind both Ben Chilwell and new recruit Marc Cucurella in the left wing-back pecking order.
The Hammers are also understood to have expressed their interest in 29-year-old Vanaken, with Sky Sports News claiming that an opening offer of £8.4m has been rejected by the Belgian outfit.
Vanaken is believed to be keen to challenge himself in the Premier League having spent his entire playing career in his native Belgium, and West Ham are expected to table an improved offer.