"The static kill operation could go very quickly," Allen said on Saturday.
Plugging the well
The operation is intended to plug the well by pumping heavy drilling mud through the blowout preventer valve system that sits on top of the well and then injecting cement inside to seal it.
BP capped the leaking well last week, choking off the flow of oil for the first time since an April 20 explosion killed 11 workers and sent crude gushing into the Gulf.
But the rig drilling the relief well and other vessels at the site, located off the Louisiana coast, were moved out of the path of the storm on Friday.
They are now returning to the site, but it will take 24 to 48 hours to get all the equipment back in place, Allen said.
The relief well is intended to intersect and finally seal the damaged well, which extends 4km below the seabed.
Once the drilling ship returns to the spill site, it has to reconnect to the relief well using 12 metre strings of riser pipe that were pulled up and stored on the rig, Allen said.
BP has said it expects to permanently plug the ruptured well in mid-August, ending the worst oil spill in US history.
But the British energy giant's response to the spill has been marked by a series of public relations gaffes by management and calls have grown for Tony Hayward, the chief executive, to step down.