The purpose would be to keep Patrick's car ranked in the top 35 in points, guaranteeing her and sponsor GoDaddy.com a spot in the starting lineup each week.
"We'd love to,'' Stewart said Friday at Bristol Motor Speedway. "If we can put together a package to run somebody in the rest of the races we'd love to do that. It's in everybody's best interest to do that.
"It would be good for us as a team to be able to go ahead and run that car full-time if that opportunity presents itself.''
Among the drivers who have surfaced is Mark Martin, who is driving the GoDaddy.com Cup car for Hendrick Motorsports this season.
Martin, 52, is looking for a part-time ride in 2012, when he is replaced at HMS by Kasey Kahne.
Patrick, who will drive a full Nationwide Series schedule for JR Motorsports next year before moving full-time to Cup at SHR in 2013, told ESPN.com she'd heard rumors of Martin's interest, but, "I really don't know.''
"It could be a great thing, though, to be able to have somebody to drive that car every week and keep it in points so I'm always in the race,'' she said. "They (GoDaddy.com) supported Mark obviously at Hendrick. Maybe that's something they are looking into.''
Sources said the key for Martin would be finding a sponsor. GoDaddy.com CEO and founder Bob Parsons was noncommittal when asked if he would sponsor the remainder of the season for the third SHR car.
Stewart said he has not set Patrick's Cup schedule yet, although Patrick said the odds of her debut coming in the 2012 Daytona 500 were good.
Dale Earnhardt Jr. , who owns Patrick's Nationwide car, said, "Daytona would be a tough deal to turn down.''
"Whatever happens is going to be good for everybody,'' he said.
Stewart said he has been working on hiring personnel for Patrick's arrival for almost a month.
"I'm excited about it,'' he said of Patrick joining SHR. "She's putting 100 percent into it and that's something that we're excited about. She definitely is deserving of an opportunity like this, and we're excited and honored that she chose us to do it with.''
David Newton covers NASCAR for ESPN.com. He can be reached at firstname.lastname@example.org.