With the club sitting at the bottom of the Premier League, speculation of a possible sacking for the Israeli manager has been relentless.
The former Chelsea and Portsmouth manager appeared to be on the brink after a 5-0 away defeat to Newcastle last week, but a League Cup Semi-Final first leg win over Birmingham has encouraged the Hammers board to keep faith with Grant, who was brought to the club in the summer following the dismissal of Gianfranco Zola.
Despite the increased speculation surrounding Grant’s job, form has generally been better of late. The Hammers loss at St James' Park was just one from their last seven games.
But failure to reach the Carling Cup final or to collect points in forthcoming fixtures could mean the axe falls on the 55-year-old.
Defeat to Arsenal at the weekend may convince owners David Gold and David Sullivan to act swiftly to appoint a new manager before the transfer window slams shut, allowing them to bring in reinforcements to get the club out of the relegation zone.
Sam Allardyce is a name that has been continually linked with the Upton Park job since being sacked by Blackburn Rovers in December.
Grant has been frustrated in the transfer market, with a deal for Steve Sidwell falling through and loanee centre-back Tal Ben Haim returning to parent club Portsmouth. The Hammers boss will, however, hope to secure a deal to bring Wayne Bridge to East-London in the next few days.