Sportsmail revealed last month that Anfield boss Hodgson had made a personal check on £15million-rated M'Vila, who is well known to Liverpool director of football strategy Damien Comolli.
In demand: Rennes forward Yann M'Vila (left)
However, reports in Madrid reveal that Jose Mourinho is also keen on a deal after identifying the 20-year-old as his new Michael Essien.
The Real boss counted Essien as one of his best signings while Chelsea boss and is an admirer of M'Vila's similar box-to-box style.
As one of Ligue 1's emerging prospects, he fits Madrid's shift of policy to signing genuine young talent - as they did with Mesut Ozil, Sami Khedira and Angel di Maria in the summer.
Diarra's future in La Liga looks increasingly uncertain. The 25-year-old former Arsenal, Chelsea and Portsmouth midfielder has started only three league games this season and will not sit on the bench forever.
As well as Liverpool, Tottenham would be keen to take Diarra on loan with a view to buy at the end of the season, while Aston Villa and Manchester United are also keen.
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Source: Daily Mail
Source: Daily Mail