The Dudley-born chief is currently working to bring in the players he believes can keep the Baggies in the Premier League.
Robert Snodgrass is due to sign today with strengthening the spine of his team Allardyce’s next priority.
Reports in the national press have suggested Newcastle’s Carroll and Everton’s Cenk Tosun are amongst the bosses targets.
But he confirmed he isn’t chasing Carroll and that Albion’s new striker will arrive from abroad.
“It’s not right, no,” Allardyce said when asked if he is interested in Carroll.
“I’m looking for a frontman, but I don’t believe Andy is available.
I think Steve (Newcastle boss Steve Bruce), like everyone else, needs his options in this difficult time.
“At this moment in time, I am not looking at Andy.
“I am looking for a front-man, hopefully, he’ll be coming through the door as quickly as possible.
“That’ll be from abroad, rather than from this country.”
Meanwhile, Albion are expected to sign former Preston North End and Wolves goalkeeper Andy Lonergan today.
The 37-year-old with strengthen the goalkeeper department and provide back-up to Sam Johnstone.
Albion currently have two back-up goalkeepers in David Button and Jonathan Bond.
But it is understood Bond will be leaving the club this month.