Kane ruptured a tendon on New Year's Day in the 1-0 Premier League defeat against Southampton and has undergone surgery. The Spurs captain is expected to be out until April while England plan for the 2020 UEFA European Football Championship.
Speaking to Chelsea's official website, Abraham expressed his disappointment at Kane's impending absence for his country but said he's willing to compete for the striking role with England's attackers.
"Of course I look up to Harry Kane and I'm gutted he's injured but hopefully he'll be back for the Euros.
"There is an opportunity and that's the world of football but there's a load of competition as well. I look across the board and see Marcus Rashford, Danny Ings, a lot of strikers scoring goals.
"Jamie Vardy is another talented striker, he has an eye for goal and he's one of the players I've grown up loving. I've got to steal his ideas and make them my own but if he comes back [from international retirement], then he comes back. Hopefully I'll still be there either way.
"I'm always ambitious and it's always at the back of my mind. Growing up, I always wanted to play for England and now I have the opportunity so I'll try to grab it with two hands. There's probably more pressure being Chelsea's number nine but I'm enjoying myself and I just have to keep doing that."
However, after an outstanding season last term with Villa in helping the team gain promotion from the EFL Championship, Abraham returned to his parent club. Chelsea were under a transfer embargo, allowing the striker a clear path into the starting XI under new manager Lampard.
Abraham has scored an impressive 15 goals and provided four assists in 29 appearances in the Premier League and Europe this term. Chelsea now have the ability to add to their forward line after a reduction in their transfer ban, but Abraham's place in the team should not be under threat.
The player had the opportunity to play for Nigeria two years ago because of his parental lineage; however, he opted to pledge his future to England. That decision could now bear fruit for both player and country. Abraham has one goal in four caps, scoring last November in a Euro qualifier.
Three Lions boss Gareth Southgate has an impressive array of strikers to call upon while Kane recovers.
Vardy is the Premier League's leading scorer with 17 goals, and Ings and Rashford are both in the best form of their careers with 14 league goals apiece. Raheem Sterling also provides Southgate with another forward option. The Manchester City player has netted 11 league goals this season.