Shots were fired at the plane as it left a military airbase near Islamabad on Friday. Police found two anti-aircraft guns and a machine gun on the roof of a nearby house.
The officials said they were looking at the possibility that militants planned Friday's attack prior to the crackdown on the Red Mosque, in which 19 people have died, but brought it forward.
"Investigators are probing whether the attack on the president's plane may have some links to the crackdown against extremists hiding in the Red Mosque," a senior security official told AFP on condition of anonymity.
Because the identities of those who lived in the house and their links to suspected militant groups are unknown, the investigation remains "open-ended'.
But an experienced and senior anti-terrorism official said it appeared that the attackers were in a hurry.
"The site and the method were of their choice, but because of the events of Red Mosque they might have advanced the plan and faltered," the official told AFP.