The 20-year-old striker is currently on a season-long loan at Swansea City, where he has impressed with four goals and an assist in 10 Premier League appearances to date.
On an international level, Abraham has been playing with England's Under-21s side for the last year and has already racked up 13 caps, but is also eligible to play for Nigeria through his father.
According to The Times, Nigeria have been courting Abraham in recent months and met with him in September in an attempt to persuade him to switch allegiance before he earns his first senior cap.
The newspaper claims that Abraham has decided to turn down their advances however, informing "senior FA officials" in recent weeks that he remains committed to the Three Lions.
England manager Gareth Southgate was in attendance at the Emirates last weekend for the Swans' 2-1 defeat to Arsenal and is believed to be considering giving Abraham a place in his squad for next year's World Cup in Russia.