"At the start of every test week we have bumps and bruises. JJ has a bit of a knock. It's nothing too serious and we are working hard to get him fit and in an England shirt this weekend," Farrell said.
"We'll give JJ every chance to prove his fitness."
Henry Slade and rugby league convert Sam Burgess are waiting in the wings if Joseph is ruled out, with Farrell's son Owen also an option.
Number eight Ben Morgan is carrying a knee injury.
"Ben has a little bang on his knee that isn't serious at all," Farrell said.
"There are still a couple more knocks, people who are not serious. We'll leave them unnamed."
England won their Pool A opener against Fiji 35-11 on Friday, but will be looking for a more convincing performance against the Welsh.
"We know what's coming. We know the game we want to play and impose ourselves," Farrell said. "We don't want to just stop Wales playing but we want to impose our game."
Wales opened their campaign with a 54-9 win over Uruguay.
(Editing by Ed Osmond)
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