Three-time world champion Sir Jackie Stewart is eager to work with Romain Grosjean and help prevent the accidents that are "jeopardising his career".
Grosjean was called a "nutcase" by Mark Webber on Sunday following a collision.
"I would love to help Romain, because I think he has enormous potential," said Stewart, an 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."
In 15 races this season, Grosjean has been involved in seven first-lap accidents and one on the second lap.
He was banned from this season's Italian Grand Prix after causing a first-corner pile-up at Spa to become the first driver to be excluded from a race since Michael Schumacher in 1994.
The 26-year-old was given a 10-second stop-go penalty following his crash with Red Bull's Webber in Japan on Sunday, before eventually retiring with two laps to go.
Stewart, who won the world title in 1969, 1971 and 1973, believes Grosjean has the potential to become one of the sport's top drivers.
"It's his first full season in F1 and he is fast enough to win races," he said. "I actually think he could have won one or two Grand Prix this season, but at the moment his potential is being overshadowed by the number of accidents he's having."
The Scotsman first offered to coach Grosjean back in July.
"He had already had a few accidents then and I thought I might be able to help him avoid them in the future," Stewart said. "I'd been a young entrant into Formula One myself and had also run a fairly good driver development programme at Stewart Grand Prix, when I'd helped drivers like David Coulthard, Juan Pablo Montoya, Gil de Ferran and Allan McNish.
"Romain, who I have to say is an extremely nice young man, chose not to take up the offer.
"The season was congested then, he was about to go on his honeymoon, and he felt he had his own people assisting him.
"When the time comes and he wants to do it, I will always be there for him because of my relationship with the team.
"For some reason, racing drivers of all kinds feel they don't need coaches once they leave karting. That's unlike any other sport I know."
The 73-year-old says Grosjean needs to curb his natural attacking instincts and show greater anticipation in races.
"Having the talent and speed to win races can be intoxicating," Stewart said.
"What all the top drivers have is very good mind management, knowing how to go about their business. It's very rare that any of them have collisions. That's obvious with Sebastian Vettel, and Fernando Alonso's collision at the first corner in Japan was a real rarity.
"The mind has to be the master over natural ability. Having been there and had very, very few collisions in my career, I know that to finish first, first you must finish, and that you never win a race on the first corner, but you'll quite often lose one there."