Len Duvall, chairman of the Metropolitan Police Authority (MPA), said on Saturday that the review was being carried out amidst "growing pressure" for a public inquiry into the policy.
The comments came as calls mounted for the head of the Metropolitan Police, Ian Blair, to resign over his handling of the mistaken killing of Jean Charles de Menezes, 27, in the tense days after July's London bombings.
Duvall told the The Independent newspaper: "I accept there is growing pressure for an inquiry. I have no objection to further scrutiny of the policy. If greater oversight of operations provides public reassurance, then that can only be a good thing."
"The MPA will be looking at these issues, and the Met (Metropolitan Police) are carrying out their own review. Ultimately, however, it is up to the government to set up a public inquiry."
The Guardian newspaper said the Association of Chief Police Officers (ACPO) was conducting the internal review.
There has been growing pressure
for a public inquiry into the policy
It said police want to keep the shoot-to-kill option but have been discussing ways to cut the risk of innocent deaths.
A senior police source and member of the ACPO, was quoted as telling the daily: "The review is not theoretical, it is looking in great depth."
The Guardian listed the issues under consideration as:
- Whether any other non-lethal weapons exist or are in the making that could quickly immobilise a suspected bomber.
- How much intelligence is needed before officers are authorised to shoot to kill.
- How to assess information fast when under pressure.
- How to ensure effective lines of communication between commanders and those on the ground.
It said the review would try to draw lessons from the 7 July bomb attacks on subway trains and a bus in the British capital and an abortive copycat attempt to attack the city two weeks later.
In addition, police would explore their methods for a planned raid against a suicide bombing suspect - so-called Operation Clydesdale.
The armed officers who shot dead de Menezes after he boarded a subway train at Stockwell station in south London on 22 July were working under Operation Kratos, which authorises them to shoot to kill.
Police shot de Menezes on a train
The Guardian, however, said top police officers who support the policy have admitted there are fears about whether using it again would end in another mistaken killing.
"There were big agonies before and Stockwell has just emphasised that," the police source told the newspaper.
Asked whether there was confidence in Kratos, the source replied: "It is very hard to view something like Kratos and use words like confidence."
In its front-page article, The Guardian said top police brass had met over the past month to see what could be learnt from de Menezes's death.
"I accept there is growing pressure for an inquiry. I have no objection to further scrutiny of the policy"
Metropolitan Police Authority chairman
Hoping to reduce the chance of more innocent lives being lost in the fight against terrorism, they would also look into intelligence gathering.
The police source was quoted as saying: "In any firearms incident the most crucial bit is the intelligence you receive. One question is how much intelligence do you need to shoot to kill. What systems are available to check out the intelligence quickly?"
A spokeswoman for ACPO told the newspaper: "We constantly review our guidelines."