Konchesky sustained a hamstring strain in the 2-2 draw with Sunderland on Saturday.
Hodgson expects the former Fulham ace to miss the Europa League clash at Utrecht on Thursday and their clash with Blackpool at the weekend.
“He’s got a hamstring strain,” Hodgson told the club’s official website.
“I couldn’t tell you exactly how bad it is yet.
“I don’t think it’s extremely bad but I certainly think it would rule him out for Thursday and next Sunday.
“Hopefully it won’t be much more problematic.”
