The 18-year-old has made the breakthrough into the first-team this season and has impressed with his displays in the Europa League, FA Cup and Carabao Cup.
However, Nelson is out of contract next year and there has been very little progress made to negotiate a new deal for the winger to remain at the Emirates.
Nelson, an England Under-19 international, has been with the Gunners since the age of nine and is highly-rated amongst the Emirates faithful.
Nelson has been tipped to have a bright future in the game and has scouted by several clubs from the Premier League and other top European teams.
The Gunners are in real danger of losing the teenager if they are unable to tie him down to a new deal, which will not go down to well with the fans.