The News of the World says the France striker has been told he can leave Old Trafford as Manchester United prepare to sign Spurs' Dimitar Berbatov.
Hodgson wants to pair Saha with his latest signing Bobby Zamora as they try to fill the void left by Brian McBride's return to America.
Saha, 29, whose time at Old Trafford has been marred by injuries, has two years left on his deal but United may be prepared to let him leave for a knockdown price.
He has not travelled to South Africa for United's tour. Bolton and Roma are also being kept informed of developments.