Abraham, who recently turned 24, has enjoyed a positive start to life in the Italian capital - scoring four goals already as he has instantly endeared himself to Roma supporters.
And the No. 9 confirmed that he has enjoying himself so far under Jose Mourinho.
“I want to be in the names of the best in the world when they’re ranking the strikers,” Abraham said.
“That’s my aim and I won’t stop until I’m there.”
He added: “I got to a point [at Chelsea] where I had to sit down and talk to myself. I was going out to train and I was doing it for me. I was going to train to better myself because it’s easy to throw a strop, to be angry around the place, to be a bad egg. For me, it was the opposite. I learned about myself and I think that strengthened my mindset.”
The move to Roma has revitalised him.
“I realised I needed to go out and prove myself," he said.
"At first I did not think much of it. I wanted to be in the Premier League and I wanted to stay here. It was home. I had to open my wings a bit and make a choice and I chose Italy and would not change it.
"Of course, there were nerves and changing countries is always a brave thing to do. But I’d recommend it to young English players. I’d say not to be scared. You learn about yourself. It’s tough but I’m getting used to it.
"I’ve gone to Rome and it’s time to show myself again.”
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The London-born man, who could add to his six international caps during the upcoming games against Andorra and Hungary, acknowledged the role Mourinho played in persuading him to make the switch.
“The first thing he said to me was, ‘Do you want to enjoy some sun or stay in the rain?’ I laughed!" he said.
“Jose had a goal. I could see where he wanted Roma to go and I wanted to be part of the process.
“He is a good man and has helped me a lot so far. I have learnt so much tactically — as much as I have in my entire lifetime. Jose said the fans would be looking at me to bring some life into the team.
"I knew from the get-go there were going to be a lot of eyes on me. I had to give good first impressions and that’s what I’ve done.”
Abraham also found himself on the back pages of many of the sports pages in England on Thursday, after becoming the first England player to confirm he is double vaccinated against Covid-19.
“It is a personal choice,” he said.
"People are entitled to do what they want to do with their bodies. For me it was a different situation. I am vaccinated. That is a personal choice. I have contracted the virus before, I am in Italy and for me it is the right thing to do.
"Everyone is entitled to do what they want to do and what is personal to them. They should make the decision to do what they want to do.”
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