The 20-year-old is a potential January target for Liverpool and Hodgson wanted to take a closer look.
M'Vila is valued at around £15 million and could represent Liverpool's key signing in the transfer window.
The Congolese-born star has won four international caps for France and could feature against England on Wednesday.
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Meanwhile, Manchester United are reportedly considering a 'cheeky' January move for Liverpool goalkeeper Pepe Reina. (caughtoffside.com)
United are looking for a long-term replacement for 40-year-old Edwin van der Sar.
Reina recently denied reports he was unhappy at Anfield, but there are thought to be plenty of big clubs ready to pounce if he decides to leave.