Correspondent Michael Schmidt cited sources in saying the sport's governing body is speeding up the process, which in theory could be pushed out as far as 45 days.
But "The process should take place before the British grand prix," said Schmidt from Montreal early on Friday.
Schmidt also reported on Friday that many in the paddock are surprised that former Ferrari team boss Jean Todt, now the FIA president, excused Ferrari from the proceedings.
Todt ruled that Pedro de la Rosa's Barcelona running with a 2011 car conformed to the rules, but it is believed that the Spaniard was running 2013-specification Pirelli tires.
"And apparently it wasn't Pirelli who paid for that test, but Ferrari," said Schmidt.
And engineers reportedly believe that a 2011 car, with a blown diffuser, is highly comparable to the downforce levels of this year's single seaters.
A rival voice in the paddock said: "Was it really a coincidence that Ferrari then won the Spanish grand prix on the same circuit?"