The midfielder is set to be at the centre of a bidding war between top Premier League clubs next summer, with Chelsea among those monitoring his situation. Manchester United and Manchester City have also both been repeatedly linked with a move for Rice.
Rice has a contract with West Ham until 2024 and, while the Hammers could trigger a 12-month extension, the 23-year-old appears to have no intention of signing a new deal.
That means next summer would represent the last chance for West Ham to secure a big fee for Rice.
Asked whether playing at the World Cup has given him the hunger to be challenging for the Premier League title and playing in the Champions League, Rice said: “Yeah, 100 per cent.
“For the last two or three years I have been saying that. I have been playing consistently well for [my] club and I feel like I really want to keep pushing.
“I see my friends here who are playing in the Champions League and for big trophies… you only get one career and at the end of your career you want to look back at what you have won and the biggest games you have played in. I am really ambitious.”
Rice has earned praise for his brilliant displays alongside Jude Bellingham at the World Cup and has increased his profile in Qatar.
He is preparing to play a key role in Sunday’s last-16 clash against Senegal and insists England are not scared about the prospect of facing a penalty shootout.
England suffered penalty heartbreak against Italy in the Euro 2020 Final but won a World Cup shootout for the first time against Colombia in Russia four years ago.
Rice is confident England are ready should it come down to spot-kicks in the knockout stage and said: “If it does come to penalties, I will back us 100 per cent.”
He added: “Since Gareth has come in, we have really shifted our mindset on penalties.
“We lost to Italy in the Euros but we beat Colombia in 2018 and it is a thing here now that we are really big on. We know we are at the stage now where we can face penalties and we will be really prepared for that.
“You do not want to over-take penalties in training, I do not think that helps anyone. You want to feel fresh, you want to have your penalty, you want to pick your spot.
“If it does come to penalties, I will back us 100 per cent. I am really confident in what we are seeing, the methods we have got and also the way the lads prepare for their penalties.”
Wales v England FIFA World Cup 2022 Qatar | Group B Match | 29th November 2022
Rice expects Senegal to be England’s toughest test yet in Qatar but he believes Southgate’s side will raise their game the deeper they go into the tournament. He also says the disappointment of being substituted in the Euro 2020 Final is fuelling his desire to help lead England to glory at the World Cup.
Rice said: “It drives me on a lot. You do not want to get taken off in any game, let alone a final. The manager saw something in that game and that is absolutely fine.
“We have got such good players, where if someone can come and do something differently than I can do and it helps the team, then I am happy with that. If that means we are going to win [a game] or win the World Cup, that is all I want to happen.
“I do not want to get brought off in any game but if the manager sees something that he thinks can change tactically, I am happy with that.”
Rice insists England are a team that should be feared in the knockout stage.
He said: “You look at our attacking players and they are world-class and we have unbelievable talents across the whole team.
“These are players who have played in the biggest games. We want to go the whole way.”