Midfielder Lanzini, who injured his thigh against Liverpool in early January, is "only a few days away" from a return to full training after missing West Ham's last five Premier League games, the club said on its website (www.whufc.com).
Striker Sakho, who has been sidelined since the end of November with a thigh muscle strain, will return to first-team training later this month.
Defenders Reid and O'Brien picked up hamstring injuries in West Ham's dramatic 2-1 FA Cup win over Liverpool on Tuesday, while James Tomkins is out for six weeks with a calf injury he sustained against Southampton at the weekend.
Kouyate suffered a mild concussion during the Liverpool game that will keep him out of action for at least six days, in accordance with Football Association guidelines.
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Amlan Chakraborty)
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