Doubts had previously emerged over Wanderers' ability to register Abraham, who has already played for Villa and Chelsea this campaign.
FIFA rules state that a player can only appear for a maximum of two clubs per season, although it is argued that as Abraham's Blues outings came in the Community Shield - which is considered a friendly competition - and at under-23 level, he should not be denied a move.
The Sun reports that despite having pushed for more than a week, Wolves have yet to hear back from world football's governing body.
However, it adds that both the FA and Premier League are happy to give the green light if required, prompting Nuno Espirito Santo's side to ask the former organisation to turn up the pressure on FIFA.
The newspaper also claims that Chelsea have until January 14 to terminate Abraham's loan deal.
The twice-capped England international has scored 16 goals for Aston Villa this season.
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