The 24-year-old was speaking at St George's Park on Thursday after earning a recall to Gareth Southgate's England squad for World Cup qualifiers against Andorra and Hungary, an achievement which vindicates his decision to leave Stamford Bridge for Italy this summer in a €40 million deal.
Abraham enjoyed a breakthrough season under former Blues boss Frank Lampard in 2019-20 before being frozen out under his successor Thomas Tuchel, starting just two Premier League matches as he battled an ankle injury.
"I've always told myself no matter how good I get, I can always get better," he said. "After my career, I can sit back and look at the things that I've done. I want to look back and say I've done everything I can, I left it all out there, I've worked as hard as I could.
"Until then, every day grafting, trying to better myself. I want to be in the names of the best strikers in the would when they are ranking the strikers. That's my aim and I won't stop until I'm there.
"The easy option would probably be just to stick around and sit down. Chelsea is a massive club. They will compete and try and win trophies so the easy option would have been to do that. But I realised that I need to go out and prove myself, play some games. I took a decision and it was the right one."
Abraham has made a bright start to life in Italy, scoring four goals in his first ten appearances but he was initially sceptical about leaving England until Mourinho intervened.
He explained: "I think the first thing he [Mourinho] said to me, I picked up the phone and he was like: 'Do you want to enjoy some sun or do you want to stay in the rain?'
"I laughed and I think at first I didn't really think much of it when he was speaking because my mindset was that I wanted to be in the Premier League, I wanted to stay here. It was home, being around London, being in England. I had to open my wings a bit. I had to make a choice and I chose Italy. I don't take it back.
"When he speaks, you listen. He's a good man and has helped me a lot so far. Hopefully we can build from there. I've learned so much tactically than I have in my lifetime. You need to learn off different managers."
Abraham scored 30 goals in 82 appearances having joined them at the age of seven but encouraged others frustrated at a lack of progress to gamble on playing overseas.
"Moving away from home and changing countries is always a brave thing to do," he said. "I do recommend going English players who listen to me or see me and the likes of Jadon Sancho [who left Manchester City to join Borussia Dortmund before returning to Manchester United] who have gone out and done it not to be scared. It is nice to go and learn a different culture. You learn about yourself. I do recommend it if that is on the table."
Asked earlier in the day about the issue of the COVID-19 vaccine and the reluctance of some players to take it, Abraham's former Chelsea teammate Fikayo Tomori revealed the England team doctor has discussed the situation with the squad.
And Abraham added: "I think it is a personal choice, really. People are entitled to choose what they put into their bodies. For me, it was a different situation. I am vaccinated. It was just a personal thing for me. [Being] in Italy and obviously, I've contracted the virus before. I thought for me, it was the right thing to do. Everyone is entitled to do what they want to do. It is personal to them. I think they should make the decision what they want to do."