The Welsh midfielder is currently sidelined by the hamstring problem he picked up against Liverpool on the first day of the Premier League season.
Ramsey is back in light training with the Gunners squad but Arsene Wenger is not satisfied with his recovery and will not risk him until he is 100% fit, according to The Sun.
The 25-year-old carried a slight problem into the season opener following a heavy summer schedule at Euro2016 with Wales, causing him to limp out of the 4-3 defeat to the Reds.
He has not featured since and is no chance of getting up for the weekend's home derby with London rivals Chelsea.
Ramsey has experienced hamstring issues in the past and it is understood that Wenger has no intentions of playing the attacking midfielder before he is fully prepared to resume at top level.