Konchesky was subsituted after 28 minutes on Saturday with a hamstring injury and will miss Thursday's Europa League game with Utrecht and Sunday's Premier League game with Blackpool but should be fit for the Goodison Park derby on Sunday, October 17th.
Daniel Agger is set to continue at left-back as Fabio Aurelio is still not fit.
"Where Fabio Aurelio is concerned, caution and prudence have to be the words that we use. He is progressing all the time and his efforts are very commendable but we can't bring him back too early," said Roy Hodgson.
"We took him off against Trabzonspor as a precautionary measure, as we didn't want to run the risk of him sustaining a serious problem."