Michael Laudrup's side drew 1-1 against Russian outfit Kuban Krasnodar in their Europa League group match in south Wales on Thursday evening, with a last-minute penalty preventing the Capital One Cup holders from making it three wins out of three in the competition.
A 2-0 defeat at Southampton followed their last Europa League outing and Hammers boss Allardyce is hoping fatigue may be a factor.
"There's a chance it can, there's no doubt about that," he said.
"Having experienced the same situation myself when I was at Bolton the most difficult game to win was always the one after we'd played in Europe.
"Michael Laudrup did make a lot of changes, six changes to the side that beat Sunderland so we'll have to wait and see.
"If there is any advantage we might be able to take with a few of their players having a bit of fatigue then hopefully we can capitalise on that.
"It's really about our players going and playing as well as they know they can and that's line has been set by the performance at Tottenham and I'll be looking for the players to achieve that at Swansea. If we can achieve that type of performance then we'll give them a hell of a game."
Allardyce has examined Swansea's 4-0 victory over Sunderland last week - their first in the Premier League since March - and was impressed.
"I think prior to the Sunderland game I would have talked to the players about any nervous frailties they (Swansea) might have suffered because of the time they have gone without winning at home," he said.
"I suppose it sounds a lot longer than it really was, because there was a break when this record was calculated from last season into this season.
"They'll have taken a lot of confidence from the fact they ended up breaking down Sunderland and getting four goals so that fear might now have left them.
"It's always a difficult game. They've had a terrific amount of progress over a few years and haven't looked back for many, many years and they have some really good players.
"Michael will be expecting them to try and turn home games into another victory and our format is to go and play like we did against Tottenham and see if we can win the game.
"Certainly we need to get some points out of it because we're way down on the points total I expected after the first eight games. It's a big game for us to make sure we play our best and get some points out of."