But Stewart only would be interested in signing Patrick to a Sprint Cup ride for Stewart-Haas Racing, which does not field a second-tier Nationwide Series team.
"Anybody that's got a Cup team that would have the availability would jump at the chance to do something with her," Stewart said Wednesday during an appearance for sponsor Office Depot's new Tech Services stores.
"You would be crazy not to entertain an offer like that and an opportunity for her to drive a race car for you."
Patrick is running a limited Nationwide schedule for JR Motorsports for a second consecutive year. She's got an option year coming up on her contract with Andretti Autosport and is deciding whether to stay in IndyCar or make a move to full-time NASCAR next year.
She said during preparations for the Indianapolis 500 last week that she doesn't know what she'll do next year.
"I suppose anything is possible," she said. "But I know for me, I haven't made any of those decisions yet."
Stewart fields two cars at Stewart-Haas Racing, but the two-time champion eventually wants to get to the NASCAR-maximum four-car limit. He's not spoken to her about joining his team, but did not know if his business managers had spoken with Patrick's team.
He also dodged any questions on if Patrick is ready for the elite Cup level. In 17 career starts, her highest finish was fourth at Las Vegas in March. She's run only four Nationwide races so far this season and has eight remaining on her schedule.
"It's just time (she needs)," Stewart said. "I didn't think I was ready for Cup and Bobby Labonte and Joe Gibbs said, 'Yeah, you're ready.'
"It took me running some Cup races before I realized I was ready. I'm not sure you know until you get out and do it. She's smart enough. She didn't get to this level by making bad decisions."
Stewart has given Patrick advice during her NASCAR trial, but the one thing he can't counsel her on is giving up on the dream to win the Indianapolis 500. Stewart won the 1997 IndyCar championship but left the series to move to NASCAR.
He's never won the Indy 500 but does have two Brickyard 400 wins in NASCAR.
"That's not an easy decision to make, but you have to think about what is best for you long term," Stewart said. "She's the only one that knows what she wants to do. Whatever decision she makes, she's going to have a reason for it."
Meanwhile, Stewart declined to comment on former Joe Gibbs Racing teammate Kyle Busch's speeding ticket Tuesday. Busch was pulled over doing 128 mph in a 45 mph zone test driving an almost $400,000 Lexus on loan from manufacturer Toyota.
Stewart, who represented Office Depot while delivering laptops, printers and a gift card to a Charlotte elementary school, cited the nature of his appearance as reason for not discussing Busch's ticket.