Frye also said the team is not certain AJ Allmendinger will be back in the No. 84 Toyota next season.
"AJ has been a Red Bull athlete for a long time. They are very found of AJ," Frye said before Sunday's race at Richmond International Raceway. "We are going through different scenarios right now and should know something shortly."
Asked if it was possible Allmendinger would not be back, Frye said "Yes, that's one of the scenarios."
The future of the team has been widely discussed since an ESPN report earlier this week that Stewart had asked Frye to manage Stewart-Haas Racing next season. The report came as Frye was traveling to Austria to discuss the direction of the race team.
Among the issues was Allmendinger, who is in the second and final year of his Red Bull contract. He's shown marked improvement this season under Frye, and the entire Red Bull organization has been considerably better since Frye's late January arrival.
Frye would not directly comment on the reported Stewart offer.
"I'm very happy where I'm at," Frye said. "Obviously there is a lot going on in the sport right now, there are a lot of flattering things being said and a lot to think about, but I'm very happy where I'm at."
Toyota Racing Development president Lee White said he was told by Red Bull executives the meeting was positive and Toyota officials are optimistic Frye will remain with the team. Red Bull struggled in its first NASCAR season last year, when team leadership operated with a Formula One mentality.
The addition of Frye, a NASCAR veteran who spent 12 years running the team that merged with Dale Earnhardt Inc. last year, has put Red Bull on the right track in its second season. Brian Vickers is 15th in the standings, Allmendinger is no longer failing to qualify for races and former F1 driver Scott Speed is quickly adapting to stock cars under Frye's developmental plan.
"I think (Frye leaving) would be a significant challenge for their evolution and improvement as a team," White said. "We are absolutely thrilled with their progress and that they are fulfilling their possibilities."
Frye said it was his first trip to Austria, where the energy drink maker is based.
"The NASCAR program is very important to their business," he said. "As a company, I wanted to understand where we're at, what's in store for the future. There is a lot going on with the company that is really good. We've made good progress. It was a very positive meeting. No matter what happens, it is great to have Red Bull part of this sport."