The 29-year-old French defender plays for Rennes and was watched by Hodgson at the weekend.
Fanni has won five international caps and is well respected in Ligue 1.
Hodgson appears to have fallen out with England full-back Johnson, after questioning his international credentials.
Johnson responded by labelling Hodgson's tactics "boring".
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Meanwhile, AC Milan are reportedly readying an escape package for Mario Balotelli. (Daily Mail)
The Manchester City striker arrived from Inter for £23 million in the summer, but has struggled with injury and is thought to be some way from contentment at Eastlands.
Milan are keen on signing the striker in the summer - and with Balotelli a lifelong fan it could proving a tempting offer.