Carroll has been blighted by injury since the Hammers stumped up a club record £15m to secure his services on a permanent basis from Liverpool in the summer of 2013 following a loan spell the previous season.
The 26-year-old has netted four times in 11 appearances this term after a delayed start to the campaign due to an ankle problem, the same number of Premier League goals as Danny Welbeck, England skipper Wayne Rooney’s current strike partner.
Uncapped duo Harry Kane and Charlie Austin have both outscored Carroll so far, but Allardyce insists the nine-cap frontman can force his way onto England manager Roy Hodgson’s radar ahead of the Euro2016 qualifier with Lithuania in March.
“He is a very hard player to play against and if he continues to keep fit and score goals I don’t see why not,” said Allardyce. “He’s been on the fringes of the squad before and then got injured so hopefully he stays fit and we’ll have to wait and see.
“I think there are a lot of contenders for the England forwards position which as an Englishman is very pleasing. It gives Roy Hodgson a lot of options which is good.”
Seventh-placed West Ham have received plenty of plaudits this season as they push for unlikely Champions League qualification, although Saturday’s draw with Swansea was the third successive game in which the Hammers have surrendered a lead.
That includes last week’s cup tie with the Toffees when Romelu Lukaku’s last-gasp strike saw Everton salvage a replay, and the 60-year-old admits his team’s inability to close matches out is becoming a worry.
“It’s a concern. In order to win football games you need to make sure you’re strong enough in both departments [attacking and defending],” added Allardyce, who hinted he will name a strong side for tonight’s clash.
“We’ve only had four clean sheets so far and that’s not good enough to keep you in the top six. If you look at Southampton, they’re up there because they’ve had 11 in 21 games. That’s why they’re in the top four and we’re not.”
Everton boss Roberto Martinez, meanwhile, did the confidence of back-up stopper Joel Robles no favours on the eve of their cup replay by revealing the club intend to sign a new keeper while No1 Tim Howard is ruled out for six weeks with a calf injury.
Martinez, who has been linked with a move for Cardiff City’s David Marshall, said: “I have said all along that goalkeeper is an area we need to look into. We need to bring in someone for the long term, so that’s why we will look into that.”