The Hammers have been long-term admirers of the Morocco international and were strongly linked with a move during the January transfer window.
A deal is now progressing as West Ham manager David Moyes looks to strengthen his defensive ranks and strike early in the summer window.
90min have reported Aguerd underwent preliminary checks in France on Thursday after the Hammers and Rennes agreed a fee believed to be worth around £30million and the defender is set to complete the second part of his medical over the next 24 hours.
A long-term contract has been offered as Moyes closes in on his first signing of the summer.
However, the move was threatened by late interest from Newcastle as they consider an alternative to long-term target Sven Botman.
The Magpies are working on a deal for the Dutch defender and have lodged several bids with French club Lille over the last six months.
There is still confidence that a move for the highly-rated centre-back can be completed amidst interest from Italian giants AC Milan.
But Eddie Howe’s side have reportedly looked to disrupt West Ham’s bid for Aguerd by making two late approaches to Rennes.
Their efforts have been unsuccessful and the 26-year-old seems highly likely to kick-off the new Premier League season in the colours of the Hammers.