According to The Sun, the young Chelsea striker is willing to quit the Blues if Antonio Conte doesn't give him assurances that he will be part of the first-team squad next season.
This has opened the door for Arsenal to make a move as Arsene Wenger looks to bolster his squad.
Despite the intensive rivalry between the two teams, Arsenal are confident they can get a deal over the line if Abraham signals his intent to leave Stamford Bridge.
The 19-year-old spent last season on loan at Championship side Bristol City, where he scored 26 goals in all competitions, breaking the record for the most goals scored by a teenager in England’s second tier.
Chelsea still hope to tempt the teenager into signing a new contract, but he will want assurances of playing time for the Premier League Champions before committing to any deal.