Frenchman Grosjean, who drives for Lotus Renault, has been involved in eight incidences in the first two laps over 15 races this season and was branded a "first-lap nutcase" by Red Bull's Mark Webber after this weekend's Japanese Grand Prix.
"I would love to help Romain, because I think he has enormous potential," said Stewart, a three-time world champion and ambassador for Lotus's owners, Genii Capital.
"Any more accidents could jeopardise his chances of driving for Lotus next season, let alone the very best teams."
"When the time comes and he wants to do [get advice], I will always be there for him because of my relationship with the team," added Stewart, 73.
Grosjean currently lies eighth in the 2012 drivers' championship.