Despite talks supposedly being at an advanced stage on Wednesday, however, Sky Sports News claims that the transfer between Premier League rivals is now in major doubt.
Speaking about the possibility of bringing in the 28-year-old earlier today, Hodgson told reporters: "I'm not prepared to talk about any players. There is bound to be conflicting reports.
"It would be very foolish of me to start commenting on anybody at the moment. We are doing it as best we can and as professionally as we can. It is better to keep quiet on the subject."
Palace and West Ham were said to have agreed on a fee of between £10m and £12m for Sakho when opening talks earlier this week.