In James' absence, Meehan's men went top of the table thanks to a 19-16 victory over London Irish, Saturday's only Premiership action.
"We are hopeful that he will be available for the match against Leeds in the European Challenge Cup in a fortnight," Meehan said.
"But if the physios deem another week is necessary or even two then so be it."
London Irish forwards coach Toby Booth admitted a top-four place was a forlorn hope after his side had to be content with a losing bonus point.
He said: "I imagine it's mathematically possible to get into the top four but whether it's really achievable is another matter. We will shift our attention now to getting a Heineken Cup qualification place."