The Gunners may make a move for the 18-year-old in the January transfer window.
The forward has broken into the Addicks first team this season, with four appearances to his name, including starts in their last two games.
That has not gone unnoticed, with the Gunners having sent scouts to attend all of those outings so far.
They have been left impressed by what the 18-year-old has to offer, with Arsene Wenger’s side now preparing to make that interest formal in the January transfer window.
Charlton are not going to give up their young starlet easily, though, with them keen to tie Lookman down to a new long-term contract to ward off interest, the Daily Mail report claims.
That is likely to be a much more difficult task if Arsenal’s interest is real, though, with the lure of the Premier League sure to be a big one for him.
He will also look at the success that the Premier League side have had in developing young talent over the years, with a number of stars having been plucked from the Football League now featuring in the Premier League because of them.