Andy Hill was left in a critical condition after his 1950s Hawker Hunter plane crashed in West Sussex, killing 11 people.
A Sussex Police spokesman said Mr Hill's condition was "improving".
"Police and investigators from the Air Accidents Investigation Branch (AAIB), who are conducting parallel investigations, are looking to interview the pilot as soon as possible," said the spokesman.
"We are not permitted to disclose his location as this is a private matter for which we do not have the family's permission."
A preliminary report from the AAIB said there were "no abnormal indications" during the flight and that cockpit cameras showed the plane "appeared to be responding to the pilot's control inputs".
The seven-page report said there had been an inspection of the plane the day before the 22 August show and that Mr Hill had carried out his own pre-flight inspection on the day.
There were no defects reported from either inspection.
Investigators from the AAIB are reviewing a massive amount of information from those at the show or nearby, including video recordings and photographs.
The wreckage of the jet is being examined in Farnborough, Hampshire.
Those who died in the crash include wedding chauffeur Maurice Abrahams 76, from Brighton; Worthing United footballers Matthew Grimstone and Jacob Schilt, both 23; NHS manager Tony Brightwell, 53, from Hove; and Daniele Polito, 23, from Worthing.
An inquest into the deaths was opened and adjourned last week. A pre-inquest review is to take place on 22 March.