Neill, who has already attracted interest from relegated Newcastle and Greek side Olympiakos, was expected to stay after Gianfranco Zola, the manager, insisted he was confident a deal could be struck.
That optimism was misplaced, however, and now the Italian is looking for replacements.
Fanni, the French international defender, could be heading for Upton Park after his agent confirmed that West Ham have targeted the player as someone able to fill the hole left by Neill.
And Bates, the Middlesbrough defender, is out of contract at the end of the month and is desperate to secure a return to the Premier League.
Dominique Six, Fanni's representative, said: "We have been in talks with several clubs including West Ham, which is an interesting option to Rod.
"Rod is crazy for English football and I know that he would be delighted to be playing his football in there."
Six added: "To my mind Rod Fanni is the same kind of footballer as Jose Bosingwa. I had already been in touch with West Ham in the past when they asked me to seal a deal with Emmanuel Adebayor, who was unhappy with his contract with Monaco.
"I have no idea whether West Ham have made a concrete offer to Rennes or not, it's business between clubs, but what I know is that the player is keen on the English market."
Gianfranco Zola, the West Ham manager, is also looking to keep the wage bill down at Upton Park and Bates would earn considerably less than the departed Neill, who was one of the highest earners at the club.