Should Sakho complete a move to Selhurst Park he would join namesakes Mamadou Sakho and Bakary Sako at the south London-based club.
Despite improving Palace's fortunes in the Premier League, Hodgson wants to add new faces to his Eagles squad and the former England boss is likely to bring in a new defender and striker.
Diafra Sakho could be staying in London for the time being - but almost certainly not with West Ham.
The West Ham United forward is the subject of a £10 million bid from Crystal Palace, according to reports.
"We are doing it as best we can and as professionally as we can".
"We didn't have enough of a certain type of player in areas of the field".
The Hammers squad is incredibly imbalanced, and the addition of a central midfielder and centre-back will be Moyes' priority this month.
However, while acknowledging that he needs to strengthen before the end of the month, Hodgson says that he is reluctant to get "tied down" with too many players.
"We have been thinking about that since I came in September and the people who are working on this, our scouting department, Doug Freedman, Steve Parish and our owners are working overtime to try and identify people".
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