The 2000 and '02 World Rally champion was knocked unconscious when his RallyCross Ford hit a concrete post during a practice run last weekend.
Gronholm is expected to stay in America with his family for a while before returning to Finland, and will miss the next round of the Global RallyCross series - which he currently leads - at Loudon next weekend.
"Of course discussion of the next race has been going on for sure, but it's one step at a time for the moment," said Gronholm. "The first step is to get home and get fully fit, then I'll go from there."
Gronholm admitted that it was frustrating to miss out on the chance to take on former WRC title rival Sebastien Loeb again at the X Games. The Frenchman dominated the event on his debut.
"I was extremely frustrated to not be able to contest the X Games, more so because I believed my preparations were excellent," said Gronholm.
"As Sebastien had come to race, I was extra hungry to perform - of course - and I went into the event with a really positive feeling, so yes, it was very annoying that it ended the way it did, but perhaps Sebastien will consider a rematch some day."