Amartey, West Ham's Andre Ayew and his brother Jordan, of Swansea, have all been excluded after requests from their clubs because of the danger of fatigue after a long Premier League season.
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Amartey and four other players will come home early and miss friendlies against the USA and Mexico in the coming days, it is being reported in Ghana.
Also, pre-season training is now only a matter of 10 days away with Leicester City players due to report back on Monday, July 3.
All the players were training in Accra, in Ghana, earlier in the week but did not travel to the US for the fixtures.
Ghana will play Mexico on Thursday in Houston, Texas, and the USA in Hartford, Connecticut, on Saturday, July 1, only 48 hours before most players are due back for pre-season training at Belvoir Drive.
But head coach Kwesi Appiah has now agreed to release the Premier League trio along with Atletico Madrid star Thomas Partey and Torino midfielder Afriyie Acquah from the Black Stars squad.
New England Revolution midfielder Gershon Koffie, David Accam of Chicago Fire, Kwadwo Poku of FC Miami and Columbus Crew trio of Harrison Afful, Jonathan Mensah and Mohammed Abu, all based in the US, will join the squad for the friendlies.
Full squad:
Goalkeepers:
Richard Ofori (Wa All Stars) and Addo Joseph (Aduana Stars)
Defenders:
Harrison Afful (Columbus Crew), Nicholas Opoku (Berekum Chelsea), Lumor Agbenyenu (Munich 1860, Germany), John Boye (Sivasspor, Turkey), Rashid Sumalia (Al Gharafa, Qatar), Jonathan Mensah (Columbus Crew, USA), Jerry Akaminko ( Eskiserhispor, Turkey), Samuel Sarfo (Liberty, Ghana)
Midfielders:
Mohammed Abu (Columbus Crew, USA), Isaac Sackey (Alanyaspor, Turkey), Ofori Ebenezer (Stuttgart, Germany), Winful Kwaku Cobbinah (Hearts of Oak), Frank Acheampong (Anderlecht, Belgium), Thomas Agyepong (NAC Breda, Holland)
Strikers:
Asamoah Gyan (Al Alhi, UAE), Majeed Abdul Waris (Lorient FC, France), Raphael Dwamena (FC Zurich, Switzerland), Kwadwo Poku (FC Miami), David Accam (Chicago Fires), Gershon Koffie (New England Revolution)