Toffees shot-stopper Pickford hurt his thigh in the Merseyside derby against Liverpool at the weekend and the club have now carried out investigations into his injury.
He has now been ruled out of action until after the next international break, leaving Everton a man down in the goalkeeping department.
Everton could dip into the free agent ranks to bring in another goalkeeper to reinforce their options.
However, it is claimed to be unlikely that they will do so at present, with the option not one that Everton are actively considering.
Frank Lampard will likely go with what he has until Pickford is back in action.
The goalkeeper has played in all six of Everton’s Premier League matches so far this season, conceding six goals in the process.
Everton remain without a win in the Premier League this season and are next in action away at Arsenal on Sunday.
