Kehrer has entered the final year of his current contract with Les Parisiens and is also attracting interest from La Liga club Sevilla.
West Ham are short of numbers at centre-back as Kurt Zouma is the only fit central defender available to Moyes.
Following ankle surgery for new signing Nayef Aguerd and injury woes for Craig Dawson and Angelo Ogbonna, Moyes wants the Hammers to push a deal for Kehrer over the line.
Given their shortage at centre-back, Moyes would prefer that the transfer be completed before the Seagulls visit the London Stadium on Sunday.
Equally at home in the heart of the defence as well as the right side, the reigning French champions would be happy to sell Kehrer for a sum of around £16m.
The Hammers played full-back Ben Johnson alongside Zouma in their opening fixtures in the Premier League, both of which ended in losses.
Brighton, their next opponents, are currently unbeaten in the Premier League, a stalemate at home with Newcastle following a win at Old Trafford.
Moyes wants to add to his centre-back options and will look to beat competition from Sevilla to sign Kehrer before the weekend.
