David Moyes has already added five fresh faces to his squad this summer, with Alphonse Areola, Nayef Aguerd, Flynn Downes, Gianluca Scamacca and Maxwel Cornet all moving to the London Stadium for a combined fee of almost £100m.
However, the Hammers remain active in the transfer market with two-and-a-half weeks of the window remaining and they have set their sights on three new signings.
According to Sky Sports News reporter Dharmesh Sheth, West Ham are in talks with both PSG and Chelsea over deals for Kehrer and Emerson respectively, while they also hold an interest in Vanaken.
Kehrer has been identified as one of West Ham's primary centre-back targets following the injury sustained to new recruit Aguerd during pre-season as well as the sale of Issa Diop to Fulham.
Aguerd tore ankle ligaments in a friendly defeat against Rangers in July and the Morocco international could now face up to three months on the sidelines.
Sheth claims that talks between West Ham and PSG over a deal for Kehrer have reached an advanced stage, with the structure of the deal - believed to be worth around €12m (£10.1m) plus add-ons - being finalised.
The 25-year-old, who has just 12 months remaining on his contract, is yet to play in any of PSG's three matches this season, with Marquinhos, Presnel Kimpembe, Sergio Ramos all preferred ahead of him by head coach Christophe Galtier.
Kehrer has featured 128 times in all competitions for the French giants since joining the club in 2018, including 34 appearances as a centre-back and right-back last season.
Meanwhile, West Ham have also entered the race for Chelsea's Emerson, with Sheth claiming that the Hammers are in talks with the Blues over a permanent deal worth £13m.
After starting only eight times for Chelsea across all tournaments in the 2020-21 campaign, Emerson was sent out on loan to Lyon last season where he enjoyed a more productive spell as a first-team player.
The 28-year-old Italy international played 35 times for the Ligue 1 outfit, but he has since returned to Stamford Bridge and now appears to be surplus to requirements under Thomas Tuchel, with Ben Chilwell and new recruit Marc Cucurella ahead of him in the left-wing back pecking order.
West Ham, who only have Aaron Cresswell as a senior left-back option, could face competition from the likes of Lazio, Roma, Atalanta BC and Nottingham Forest for Emerson's services.
Another player who has recently emerged as a Hammers target in Brugge midfielder Vanaken, with Sheth reporting that the West Londoners have admired the 29-year-old Belgium international for some time and have previously attempted to sign him.
Vanaken has spent his entire senior career in his native Belgium and has plied his trade with Brugge for the last seven seasons.
The attacking midfielder has recorded a total of 101 goals and 72 assists in 342 appearances for Brugge, including at least 15 strikes in each of the last five seasons.
It remains to be seen whether Brugge would be willing to let Vanaken leave the club this summer, having already allowed star attacker Charles De Ketelaere join AC Milan.