However, the former Williams driver left the door open by suggesting that the decision was valid "for now".
The Woking team announced on Friday that the 2022 Le Mans winner will be a reserve driver in 2024, with a simulator role and testing.
On Saturday, there was a stir in the paddock when Toyota Motor Corporation chairman Akio Toyoda, also known as Morizo for his own racing activities, appeared in the McLaren hospitality area. He spoke to local media and was interviewed alongside Hirakawa.
His presence inevitably sparked suggestions that McLaren has an interest in enticing Toyota back to F1 at some point after the new power unit rules come into play in 2026 and that the Hirakawa deal is a starting point.
Toyota enjoyed a close relationship with McLaren for many years regarding the use of its Cologne wind tunnel, with the deal ending this summer when the team's own facility came on stream.
The team's previous boss Martin Whitmarsh spoke to Toyota in the build-up to the arrival of the new hybrid regulations in 2014, prior to doing a deal with Honda.
However, Nakajima, who serves as the company's motorsport senior executive advisor, insisted that Toyota currently has no plan to return to F1 for the first time since withdrawing its works team at the end of 2008.
"For now, it's clearly no," he said when asked by Motorsport.com about Toyota's interest in F1. "This deal is really purely focusing on a driver, supporting a driver's dream.
"At the moment, it really has nothing to do with that. I know, of course, you can think about it, and there are a lot of rumours. But I can clearly say that it's no, and nothing to do with it. For the future, we never know."
With a packed motorsport programme in other categories, Nakajima added: "Our focus now is WRC and WEC.
"In both categories, we believe that it's a really good field to have good feedback to the road car, and making ever a better car from motorsport is the philosophy of Toyota. So right now, this is the situation, and we are happy with what we have.
"So basically, the intention of Morizo-san is that he didn't want to block the path of the drivers, because Toyota is not in of F1. So this is something totally different.
"And actually, as a former driver, and as I'm involved in drivers' development right now. I really feel happy and I really appreciate Morizo-san's wish and will to support the driver's dream, even if it's not totally relevant to the activity as a manufacturer."
Explaining how the Hirakawa deal came about Nakajima said that company chairman Toyoda was fully behind it.
"McLaren is not how to say completely a stranger to us," he said. "So we had some conversation about the possibility for Ryo. And the trigger was that McLaren showed interest in Ryo. So this is how it started.
"Our philosophy within Toyota Racing, which is coming from Morizo-san, is a driver-first approach. We are trying to be driver-oriented.
"Morizo's-sans wish was basically, to give any kind of possibility for drivers for them to be better or develop themselves.
"And obviously, F1 is at the top of the pyramid, it's a place that every driver aims for. So Morizo-san had a strong wish that he wanted to support this programme.
"So our mission is really to support Ryo for him to basically settle down in McLaren and also to find as much opportunity as possible as a third driver, simulator sessions, or testing or whichever we can find. We are here to basically support this activity."
Nakajima played down the suggestion that it may be too late for Hirakawa, who turned 29 in March.
"Sometimes in motorsport age doesn't mean everything. As we can see, Fernando is still on top. So I think it doesn't matter too much for Ryo.
"And of course, for every driver, there's a right moment. So if it was 10 years before, maybe it was not the right time for Ryo. I believe this is the right time for him to jump into F1 with his experience in F1."
