Six wins from their last 10 games has seen the Hammers climb away from trouble and they are currently seven points above the drop zone.
But weekend wins for the likes of Fulham, Cardiff and Crystal Palace have got the Upton Park boss looking over his shoulder again.
Sam Allardyce: "The results some of the teams below us pulled off, some surprisingly, means we are not mathematically safe.
"If they then get back-to-back wins you have to look down and say we're not quite there. We've got five very tough games to go, we've got to try to pick up as many points as we can.
"People may have been disappointed that Arsene Wenger hasn't won anything over the last few years but he can put that right this year with an FA Cup final appearance.
"A lot of the focus is finishing in the Champions League but also making sure they win the FA Cup. And if he does both, compared to the other years, he will have had a more successful season."
Premier League
11 West Ham 37
12 C Palace 37
13 Hull City 36
14 A Villa 34
15 Swansea 33
16 West Brom 33
17 Norwich 32
18 Fulham 30
19 Cardiff 29
20 Sunderland 25
Relegation run-in
SUNDERLAND (Pld 32 Pts 25 GD -25)
Apr 16 - Manchester City A
Apr 19 - Chelsea A
Apr 27 - Cardiff H
May 3 - Manchester United A
May 7 - West Brom H
May 11 - Swansea H
CARDIFF (Pld 34 Pts 29 GD -34)
Apr 19 - Stoke H
Apr 27 - Sunderland A
May 3 - Newcastle A
May 11 - Chelsea H
FULHAM (Pld 34 Pts 30 GD -40)
Apr 19 - Tottenham A
Apr 26 - Hull H
May 3 - Stoke A
May 11 - Crystal Palace H
NORWICH (Pld 34 Pts 32 GD -27)
Apr 20 - Liverpool H
Apr 26 - Manchester United A
May 4 - Chelsea A
May 11 - Arsenal H
WEST BROM (Pld 33 Pts 33 GD -11)
Apr 21 - Manchester City A
Apr 26 - West Ham H
May 4 - Arsenal A
May 7 - Sunderland A
May 11 - Stoke H
SWANSEA (Pld 34 Pts 33 GD -4)
Apr 19 - Newcastle A
Apr 26 - Aston Villa H
May 3 - Southampton H
May 11 - Sunderland A
ASTON VILLA (Pld 33 Pts 34 GD -14)
Apr 19 - Southampton H
Apr 26 - Swansea A
May 3 - Hull H
May 7 - Manchester City A
May 11 - Tottenham A
HULL (Pld 33 Pts 36 GD -6)
Apr 19 - Arsenal H
Apr 26 - Fulham A
May 3 - Aston Villa A
May 6 - Manchester United A
May 11 - Everton H
CRYSTAL PALACE (Pld 33 Pts 37 GD -15)
Apr 16 - Everton A
Apr 19 - West Ham A
Apr 27 - Manchester City H
May 5 - Liverpool H
May 11 - Fulham A
WEST HAM (Pld 33 Pts 37 GD -7)
Apr 15 - Arsenal A
Apr 19 - Crystal Palace H
Apr 26 - West Brom A
May 3 - Tottenham H
May 11 - Manchester City A