The talented forward scored two goals in a match-winning display against Houston Dynamo last week but injured his quad whilst scoring his second goal from the penalty spot.
Union boss John Hackworth had his fingers crossed regarding Adu's fitness for the trip to Columbus on Saturday but was remaining realistic about the 23-year old.
"Freddy is coming along slower than we would have hoped," Hackworth said.
"Hopefully Freddy can be available by Saturday but we're not going to push it. He was able to get through a full workout today but he's a little behind where we thought he'd be."