The January signing has sent out words of warning to those at the Hawthorns.
Tony Pulis's side currently sit 13th in the top flight, eight points clear of the relegation zone and, to all intents and purposes, looking relatively safe.
But all it takes is one or two results that can cause a domino effect. And two results that wouldn't have pleased anyone at West Brom were their last two - a 2-1 defeat at Aston Villa in the league and a 2-0 loss against the same local rivals in the FA Cup.
As such, midfielder Fletcher has warned his West Brom team-mates they must get as many points on the board as possible in advance to avoid the drama of a last-minute dogfight to stay up.
“There is so much still for us to play for this season and we need to be clear about the job in front of us," the Scot told reporters.
“We have to keep on putting points on the board week by week and, the sooner we can get ourselves up to 40 points, the better.
“We don’t want to be waiting until the end, we don’t want to be taking things down to the wire, we want to get our points as quickly as we can, get as many as we can and finish as high up the league as we possibly can.”
Memories of Bryan Robson keeping West Brom up on the last day of the season in bygone days will no doubt bring a smile to supporters' faces.
Equally, however, there is the memory of the Baggies actually going down after miserable Premier League campaigns. As Fletcher is keen to point out, then, safety needs to be wrapped up as soon as possible...