In July, the 20-year-old signed a five-year deal at Stamford Bridge on the same day he left on a season-long loan for Swansea City.
Abraham has impressed in a struggling Swans side, netting four goals in 11 Premier League appearances - form that was rewarded with his maiden England call-up for the friendlies against Germany and Brazil.
"My main focus is Swansea but pushing on, my main target is to be in that Chelsea squad," he said in a media conference on Monday.
"It's not going to be easy, you look at the players that are there, but you have to keep pushing and keep working as hard as you can.
"I want to show the world what I'm truly made of. Of course it will be difficult, you're playing in one of the best leagues in the world.
"In the Premier League you're playing against some of the best defenders in the world but it's nice for me to have that competition.
"Gareth [Southgate] is a manager who likes to bring up young talent and that gives us a lot of confidence."