Grant was given the boot an hour after the 3-2 defeat at Wigan confirmed their relegation to the Championship.
Speaking on Twitter, Hammers co-owner David Gold described the result as "undoubtedly the worst moment in all the years I’ve been supporting West Ham".
According to talkSPORT, former England boss McClaren will be confirmed as the new manager shortly. Bookies make him the clear 1/3 favourite.
McClaren has been without work since being sacked by German side Wolfsburg in December.