Red Bull tested an 'aeroscreen' fitted to the front of the cockpit in Friday practice at the Russian Grand Prix while Ferrari tried out a 'halo' device in pre-season testing in Barcelona.
Whiting told reporters in Sochi that it “would be unreasonable” to leave a decision any later than July 1 because teams needed to incorporate the new device into their 2017 designs.
New rules, aimed at making cars faster and more exciting with wider tyres and revised aerodynamics, are being introduced for 2017.
“There are different load cases for each design because the halo has a central mounting and the 'aeroscreen' has two on the sides with nothing in the middle,” Whiting said.
Whiting, who also oversees safety for the FIA, said only one of the two concepts would be taken forward with a likely sole supplier. The FIA's F1 Commission will make the final decision.
Before then, further tests will be carried out to ensure there is no risk of the driver's head hitting the structure in an impact.
“What we are doing is some sledwork with a dummy to try to simulate more precisely just how much room you need in order to make sure that the driver's head doesn't make contact with it - as they are both substantial structures,” Whiting added.
“That is the next phase of work, which I am told should be completed within two weeks.”
Red Bull were also seeking special coatings for the interior and exterior of the 'aeroscreen' to reduce glare and ensure nothing sticks to it. The halo has no screen.
“It's quite difficult where you have tall buildings, trees, low sun, those sorts of effects, that you will probably get in Monaco and Monza, where there are natural features,” Whiting said of the screen.
Improving head protection has become a priority after the deaths last year of Briton Justin Wilson, who was hit by debris in an IndyCar crash, and Frenchman Jules Bianchi.
Sunday also marked the anniversary of the 1994 death of Brazilian triple champion Ayrton Senna at Italy's Imola racetrack.
The front wheel of the Williams bounced back in that impact with the wall, with Senna's helmet penetrated by a suspension arm.
Original source: More testing for F1's new 'halo'