The 24-year-old joined Arsenal earlier this month from West Ham in a deal that could be worth up to £105 million ($135m), eclipsing the £100m Manchester City paid Aston Villa for Jack Grealish in 2021.
The fee for Rice shatters Arsenal's club record -- previously the £72m paid to Lille for Nicolas Pepe -- and will raise expectations on a team which finished second to City in the Premier League last season after leading for the majority of the campaign.
In an interview with ESPN, Rice reflected on his rise to prominence after breaking into the West Ham team and establishing himself as a senior England international.
"I think five years ago I'd be dreaming about where I am now," Rice said. "I don't actually think about it. It is crazy to think 'yeah OK, I've been sold for £100m' but I haven't thought about it once.
"That's a price tag that is now attached to me. I just try to play football and enjoy myself. I don't try to put any added pressure on me. Me being myself is what's got me here. That isn't going to change now I'm at Arsenal. I'm still going to do things that I've done that have got me to Arsenal.
"I'm [also] going to do things differently that Mikel wants me to do and take it all in my stride and try not to put myself under any pressure. In football it is easy to do that. I think it is important that we are constantly open to learning and wanting to improve.
"At the end, judge me on the price tag then, don't judge me after two or three weeks. Hopefully at the end, that's why I've come to Arsenal because I want to be a success and I want this club to be a success."
Rice was released by Chelsea aged 14 amid concerns over his physicality but he later joined West Ham, rising through the ranks to become captain for the first time at 20 years old, going on to lift the club's trophy in 43 years as they won the Europa Conference League in June.
Having carved out a piece of history as the most expensive English player ever, Rice said: "For me, that's such a proud moment. All the hard work that you've put in, from the moment you kick a ball, through the academy systems, all the coaches that you've worked with, the people you've learned stuff off, to get to this point where I am now is really special of course.
"It is important not to put pressure on yourself. I don't do that at all, I try to take it all in my stride. There is going to be a lot of noise around me, around the transfer, around the price. But if I keep doing what I've been doing for the last couple of years that's got me here, I'm not going to have any problems at all. I just need to stay focused and just try to be as relaxed and as open-minded to working as possible."