Abraham was rewarded with a place in Gareth Southgate's England squad for friendlies against Germany and Brazil as he looks to grasp every opportunity to improve his chances of cementing his place at Chelsea.
"My main focus is Swansea but pushing on, my main target is to be in that Chelsea squad," he told reporters.
"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.
Abraham is one of 34 players Chelsea currently have out on loan, with the London club often criticised for not showing enough faith in the young players.
He could be in line for an England debut in either of the next two fixtures, with striker Harry Kane ruled out after sustaining a knee injury.
"I feel like I'm ready but it won't be easy," Abraham said on the prospect of making his England debut. "I will have to keep proving to the manager why he picked me and working as hard as I can.
"It would be a fantastic thing for me, big confidence boost to show I'm going in the right direction."
England host Germany on Friday and meet Brazil four days later.
(Reporting by Hardik Vyas in Bengaluru; editing by Amlan Chakraborty)
