Valencia joined West Ham from Mexico's Pachuca last month, having scored all three of Ecuador's goals at the World Cup finals in Brazil.
The 24-year-old is not expected to be fit for the season opener at home to Tottenham Hotspur on Aug. 16 and the trip to Crystal Palace a week later.
"The player we've spent the most money on, Enner Valencia, is our big summer signing and he is about two or three weeks away from being able to play, because he was at the World Cup," Sullivan told the club website (www.whufc.com).
"He's now in full training but I think the earliest he'll play is in the Capital One Cup match, so it'll be exciting for people to see him make his debut in that match."
The club, who also signed Argentine Mauro Zarate, have been rocked by another injury to target man Andy Carroll. He has been ruled out for four months after tearing ankle ligaments, and he missed much of last season with a heel problem.
Sullivan said West Ham had made a number of bids to bring more attacking players to the club, who finished 13th last season.
"We've got offers in for three or four strikers - one in England, three abroad - and we just hope to land one of them. We do need to sign another player," he said.
"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 but we're pleased with what we've got - there are players with massive potential for the future but we know there isn't enough goals in the team at the moment."
(Reporting by Josh Reich; editing by Robert Woodward)
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