On-loan with Swansea City, Abraham also qualifies for Nigeria and was wanted by the Super Eagles.
However, The Times says Abraham, 20, has told senior FA chiefs that he is committed to England.
Abraham has won 13 caps for England Under-21s and is willing to wait for a senior call-up rather than joining Nigeria.
The striker is in line for an England call ahead of this month's friendlies against Brazil and Germany.
Abraham denied claims he was pushing for a Nigeria switch back in September.
"Contrary to reports in the media today I would like to clarify that I have not agreed to switch my national team allegiance," said Abraham.
"I can confirm I met the President of the NFF after our last game against Tottenham at Wembley on Saturday given he is a friend of my father.
"However, any suggestion that I have made a decision to change my international representation is incorrect and wide of the mark.
"I have informed The FA that I remain available for selection for England."
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