The Belgian striker was forced off at half-time during Sunday’s 1-1 draw with Norwich City at Anfield after feeling a strain in the opening 45 minutes on Merseyside.
Benteke is set to undergo a scan on his leg on Tuesday to assess the seriousness of the problem, McAllister said as he addressed the media in the build-up to Liverpool’s League Cup third round clash against Carlisle United.
McAllister also revealed that Jordan Henderson’s operation on his broken metatarsal has been a success.
McAllister told the pre-match news conference at Melwood on Tuesday morning: “Christian will have an MRI scan today and hopefully they’ll find the problem – he’s got a little problem with his hamstring.
“Everybody [else] is good. Jordan’s come through fine. There’s not really a timescale on that, but everything went well there.
“We’re picking from nearly a full squad [for Carlisle].”
Liverpool’s 1-1 draw with Norwich left them down in 11th place in the Premier League table after having taken eight points from their first six games.
The Reds are next in top-flight action when they host Aston Villa at Anfield on Saturday lunchtime.