Lampard, who suffered the injury in training last Friday, is rated as 50-50 to play against Russia, although he will definitely not be in McClaren's plans for Saturday's Wembley encounter with Israel.
The former Middlesbrough boss told a press conference: "Frank came and joined us last night, we looked at the scans and have liaised with Chelsea.
"He's gone back there for rehab - the injury is not as serious as we first thought, although hopefully we'll assess him on Saturday.
"He may be 50-50 for next week - and Chelsea are giving him every chance of being available for us."
McClaren is confident Steven Gerrard, who broke a toe in last month's Champions League clash between Liverpool and Toulouse, will play against Israel, even though the midfielder missed training on Tuesday.
He added: "All being well Stevie G will be available on Saturday. I want him to play, the team do, the fans do and so does the whole country.
"We need big players and Stevie G is one for us. We're assessing it day by day. He's getting better and hopefully by the end of the week we'll have a better idea."
