The Sun reports that Tottenham also held an interest in the 16-year-old, but it is now between Arsenal and Wolfsburg for his signature.
The youngster’s advisor, Gaffar Liameed, said: “We had many offers for Victor, but narrowed it down to Wolfsburg and Arsenal.”
The report states the Nigerian is more tempted by the prospect of a move to the Emirates, despite visiting the Bundesliga outfit.
Osimhen claimed the golden boot at the Under-17 World Cup in Chile in November as the Eaglets romped to an impressive tournament victory.
Arsenal boss Arsene Wenger has been short of options in attack this season, with England striker Danny Welbeck yet to feature this campaign and Theo Walcott only recently returning from a two-month layoff.
The Gunners host Manchester City in a pivotal top-of-the-table clash on Monday night with both sides looking for three points in order to stay in touch with league leaders Leicester City.