The former Three Lions striker thinks that the national team will fall short of their performance in the last two tournaments as they lack the quality of the top nations.
Shearer pinpointed England's defence as a weakness and fears it will struggle against the very best in Qatar.
He said: "I don't see us going as far as we have done in the last two tournaments.
"I think in terms of midfield positions and forward positions Southgate will be confident but in terms of defensively, that's an area for concern.
"We should win the group with the ability that we have in our squad. The further you go in the tournament the better the opposition are going to be and the players you're up against, so my concern for England would be defence."
Pressed on how far England can go, Shearer said: "I'd say maybe a quarter-final."
Shearer does not envy England boss Gareth Southgate as he will have to make some "big decisions" over who will be starting matches and the team's tactical approach.
He said: "I think he's got some big decisions to make in terms of the 11 he starts and what system he's going to play.
"It's probably been made slightly easier for him now he can have a squad of 26 rather than 23. We have got one or two injuries which he has to make a call on because maybe two or three players haven't played for six or seven weeks.
"With the success that they have had in the last two tournaments we want England to go that one step further and try and win it. Whether we can or not remains to be seen. It's going to be very, very difficult."