Stoke's Peter Crouch is the Hammers' main target, but reports state that interest has also been shown in Hugo Almeida of Besiktas, while Samuel Eto'o has also been linked with a move to Upton Park.
Carroll has been ruled out until November after sustaining an ankle injury during the pre-season tour to New Zealand.
"We've got offers in for three or four strikers - one in England, three abroad - and we just hope to land one of them," Sullivan told the club's official website.
"We do need to sign another player
We have worked 24/7 all summer and we still want to get at least one more striker in
It's been very, very tough.
"We're pleased with the players we've got - players with massive potential for the future - but we know there aren't enough goals in the team at the moment.
"Pre-season hasn't gone quite as planned
The worst thing is that we picked up injuries, in particular to Andy Carroll who is out for four months and makes a huge difference to us."
Enner Valencia and Mauro Zarate are the key names among the six new arrivals at West Ham this summer, but £13million Ecuador striker Valencia will miss the start of the season after being involved in the World Cup.
Source : PA
Source: PA