Grosjean has so far enjoyed a strong first half of the campaign, finishing on the podium for Lotus in Bahrain and Canada to lie seventh in the standings with 61 points.
The Frenchman, however, has been involved in incidents which have potentially cost him points, resulting in Stewart coming forward to assist the 26-year-old.
Working as an ambassador this season for Lotus team owners Genii, the 73-year-old this week remarked: "I said to Romain it would be a good idea if he came up home one day for lunch so we could have a bit of chat.
"It is ridiculous in Formula One we don't have coaches. I am not looking to be a coach, but I know I can help him.
"Racing drivers historically have not been great listeners, but I think I might be able to help."
Grosjean has confirmed working with a mental coach from 2007 to 2009 when he was in Formula Three and GP2, but sees no need to work with Stewart on this occasion.
Recent newlywed Grosjean said: "He did offer, but the main issue is the schedule. It's very tight at the moment and I've a honeymoon to do.
"Obviously, it's very nice to have comments like that from a triple world champion.
"Let's see in the future. At the moment it's race after race, and the schedule is tight.
"You can always change. I used to work with a mental coach, but I don't feel I need one today.
"Maybe I'll feel different in the future. Things can change from week to week, but at the moment I'm happy with the way things are going."
Grosjean concedes the team environment, and not least a raft of computers, aids a current Formula One driver.
"I appreciate other sportsmen have coaches to tell them what to do," said Grosjean, referring to the likes of tennis and golf.
"We have the data and the computer, which is good for the driving point of view.
"Other sports they have a coach to tell them to put more slice on a ball or get a little closer to it, stuff like that.
"But racing is a bit different than other sports.
"Obviously it's also about trying to stay relaxed, trying to manage your stress, those kind of things.
"To be honest, with the people around me at the moment, with Gravity (his management company), with friends I can have at the track, the engineers, everything is going quite well.
"Right now I don't think I'm over-stressed or whatever, so I'd rather not change too much at the moment. I'm not going to see a mental coach again.
"Maybe in three months I will say I want to work with somebody. It's how you feel inside."