The England international has been out of the country on holiday but Press Association Sport understands he will fly in for his physical assessment with the Hammers on Tuesday.
Carroll missed the national team's end-of-season friendlies against Republic of Ireland and Brazil with a heel problem, with fears it could sideline him for up to four months.
It remains to be seen whether that has much effect on his medical but with a £15 million-plus deal agreed several weeks ago Liverpool will be keen for the move to go through as soon as possible so they can continue with manager Brendan Rodgers' squad strengthening.
Sporting Lisbon defender Tiago Ilori and Sevilla midfielder Luis Alberto, both 20, are likely to be the first to be completed but negotiations are also continuing over a deal for Sunderland goalkeeper Simon Mignolet with the future of Jose Reina yet to be decided.
Shakhtar Donetsk's £20 million-rated forward Henrikh Mkhitaryan, who scored a Ukrainian Premier League record 25 goals last season, increasingly looks like being the club's preferred attacking option with Luis Suarez so publicly courting Real Madrid.
At the back the situation is less clear as Schalke are seemingly not prepared to sell the Reds' primary centre-back target Kyriakos Papadopoulos for the Merseysiders' valuation of about £12 million, despite the player having been sidelined by a knee injury since November.
Having also cooled their interest in Swansea's Ashley Williams, with whom Rodgers has previously worked, after deeming the asking price not value for money other avenues are being explored.
Ajax's Toby Alderweireld has been linked with a move to Anfield but he has already had preliminary talks with German side Bayer Leverkusen.
Liverpool's recruitment has continued off the pitch, however, after they brought in Andy Hughes, formerly of Guoman and Thistle Hotels, as their chief financial officer to replace Philip Nash, who stood down in February.
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