The Hammers are rooted to the foot of the Barclays Premier League after a dismal start which has seen them pick up only one point from five matches.
Despite last week's 1-1 draw at Stoke, and public votes of confidence from club chairmen David Gold and David Sullivan, pressure is still on the Israeli, who signed a four-year contract to succeed Gianfranco Zola this summer.
Failure to take anything from a hotly-contested derby against the Hammers' bitter local rivals Spurs will only add further questions about Grant's future at the club.
Spurs boss Redknapp, who worked alongside Grant during his time at Portsmouth, is convinced that the 55-year-old is the man to drag his former club out of the relegation zone.
"I don't see why you'd give someone a job and then consider letting them go after three or four weeks," said Redknapp.
"He has only just got there. That doesn't make sense. I'm sure he will do a good job there.
"I think he's there for the long-term. He'll do a good job there if he's given time."
Source: PA
Source: PA