The Welshman is progressing slower than expected as he looks to recover from a thigh injury, while Tomas Rosicky is also a doubt for the derby meeting
Arsenal had been hopeful that the midfielder could return for Sunday's clash against Tottenham at White Hart Lane.
Arsene Wenger said last week that Ramsey was a "a week away" from full fitness.
But the Welshman, who has been out since Boxing Day with a thigh injury, is believed to be progressing slower than expected and, while he has not suffered a fresh setback in his recovery, Wenger is keen to ensure he is not rushed back into action.
Ramsey is not expected to be part of the squad for Sunday and is now targeting a return in the Premier League clash against Chelsea six days later.
Fellow midfielder Tomas Rosicky is also understood to be a doubt for the derby after sustaining a groin problem during Arsenal's Champions League exit on Tuesday night.
The Czech international will undergo further assessment as the Gunners count the cost of the 1-1 draw at Bayern Munich.
Mesut Ozil could also be out for more than a month with the hamstring injury that forced him off at halftime in the Allianz Arena.
Ramsey's absence has been sorely felt in recent weeks. Arguably Arsenal’s outstanding player in the first half of the season, he has been sidelined since December 26 with a thigh problem, which, as revealed by Goal, he then aggravated when he returned to full training at the end of January.
Wenger ruled Ramsey out for a further six weeks but there were private fears he could be out for even longer as Arsenal struggled to find the cause of the thigh problem that has intermittently affected the player for much of the season.
If Ramsey returns against Chelsea on Saturday week, it would come nearly three months after he last featured for the first team.