Mitroglou has scored 22 goals in 39 appearances while on loan to Benfica this season and the Lisbon side have an agreement to make the deal permanent at a cost of £7 million, the report claims.
However, it doesn't appear to have stopped the Gunners from making an enquiry, though it is said that no formal offer has been made.
The west Londoners were subsequently relegated to the Championship and Mitroglou returned to Olympiakos on loan last season, with 19 goals in 33 appearances underlining the 28-year-old's striking credentials.
Mitroglou, who has two years left on his Fulham contract, isn't the only Cottagers player being linked with a move to the Emirates Stadium, with the Telegraph reporting Arsenal interest in teenager Ryan Sessegnon on Tuesday.
The highly-rated left-sider was the captain of England's Under-16s.
The newspaper claims Leicester defender Ben Chilwell is also on the Gunners' radar this summer.