The Mirror says home-grown English striker Simpson, 21, scored a first half brace as Arsenal cruised to a 4-0 victory at Barnet on Saturday in their opening pre-season friendly.
Simpson, who has been loaned to West Brom and QPR in the past two seasons, now hopes to be included in the Arsenal squad travelling to Austria today.
Simpson has 12 months left on his contract at The Emirates and has only ever made one start for the club in the League Cup.
But Arsenal fans were chanting: 'Arsene give him a chance, Arsene, Arsene give him a chance' against Barnet.
And the youngster hopes to keep his place when Arsenal play away at SK Sturm Graz on Wednesday.
But Championship clubs like QPR and Millwall continue to monitor him.