Monger has been in the Queens Medical Centre in Nottingham since his massive accident at Donington Park last month, which led to both of his lower legs being amputated.
Crowdfunding in support of the teenager reached the Â£800,000 mark yesterday, more than three times the initial target set by his JHR Developments team, led by Steven Hunter and Tom Ingram.
That has become the fastest personal fundraising campaign ever in the Just Giving site's history, with half a million pounds raised in the opening 22 hours following its launch.
Monger told the Press Association: "All the support just makes me more determined to get back in the car and get racing again. That's the goal."
Commenting on F1 world champions Jenson Button and Lewis Hamilton showing their support, he added: "It was weird, seeing them giving their support because they're obviously people you want to, you aim to be like them, at the top of the sport. That was cool."
Monger, whose right leg was amputated below his knee and left leg further up his thigh, has chosen ocean blue metallic as the colour for his new wheelchair.
The former Ginetta Junior racer has received support from across the global motorsport community, with #billywhizz stickers adorning multiple Formula One cars during last weekend's Russian Grand Prix.
"It was very hard at first, but to see him how he is now after three weeks is just amazing," commented Billy's father Rob.
"Everyone at the hospital has been superb – if you had all the money in the world you couldn't pay for a better service than we have had here.
"He has always had the passion and no matter what happens it will always be there. If he wants to get back in the car, that's fine by me."
This weekend marks the first TOCA meeting since the accident, with all cars across the BTCC and support series carrying special #billywhizz decals, while there is an open public fundraising circuit walk taking place this evening.
Kirsty Measures, a staff nurse on Billy's ward, said: "When Billy first came in he was quite unwell … he struggled to get to grips with what happened to him. But he has overcome it.
"Every day he has had a smile on his face, he's just accepted the situation and even during the hardest times he's still managed to have a laugh and a joke about it. Checkeredflag.co.uk