Gunners boss Arsene Wenger raised eyebrows in the summer with the decision to only add Petr Cech to his ranks, and the Frenchman has just Theo Walcott and Olivier Giroud to choose from as centre-forwards.
Alexis Sanchez primarily plays wide left in a 4-3-3 formation for Wenger's side, but the ex-Barcelona star is an option for the North Londoners in a central role.
Both Giroud and Walcott were on target in Saturday's 2-0 win over Stoke City, but Shearer is not sure about either's long-term suitability to lead the line for a team who have pretensions on winning the Premier League.
Ex-Newcastle striker Shearer finished his career with 260 top-flight goals and thinks that strikers should be hitting the 30-goal tally for a side that creates as many chances as Arsenal.
The former England captain told BBC Sport: “I think a top, top striker could and should score at least 30 goals with the number of chances that Arsenal create in a season.
“I look at Theo and I think he’s too nice. If he scores, he scores and if he doesn’t he won’t lose any sleep over it and he’s got to get a nasty streak in him and I think it’s there.”
Giroud ended a nightmare week that saw him booed by his own France fans during the international break, by netting in the second half with a near-post header after Walcott's opener, but question marks remain over the pair.
Both missed chances at the Emirates in a game that could have seen Wenger's men cruise to victory by a big margin.
Arsenal return to action on Wednesday when they travel to Dinamo Zagreb on Wednesday.