The Hammers are currently shorthanded in the centre-back department with most of their senior players in that position sidelined owing to fitness issues.
West Ham are also set to see Issa Diop move to Fulham on a permanent deal having reached and agreement with the Cottagers, which means that yet another vacant spot has opened up in their backline.
The Irons have identified PSG defenders Abdou Diallo and Kehrer as two potential signings as they look to bolster their defence.
West Ham have been in talks with the Ligue 1 giants over a move for Kehrer and they have now stepped up their efforts as they want to bring in a centre-back before Sunday’s trip to Nottingham Forest.
David Moyes’ side have submitted a bid for the German’s services and are waiting for PSG’s response.
PSG have been looking to offload Kehrer this summer and it remains to be seen whether they will agree to the terms proposed by West Ham for him.
West Ham also have other centre-back targets on their radar that they could turn to in case they fail to agree a deal with Les Parisiens for him.
