The Abuja Stadium pitch has slipped into disrepair, forcing the senior national team to move their games to Calabar.
Repair work on the facility has started, with the Super Eagles expected to host Arsenal there in August, but Abdullahi insists that there would be no hurry
"I was told that Arsenal would be playing the Super Eagles in Nigeria. We know it is a club playing a national team, not a case of Nigeria playing England," he said.
"We are talking about the state of the National Stadium pitch and I think it has nothing to do with Arsenal.
"Whether Arsenal is coming to play or not, I think we should be able to put our pitch in proper shape.
"We have started work on the pitch. We want to come up with a clear strategy on how to put up an enduring job that will ensure a lasting solution to the state of pitch. If we rush it now because Arsenal is playing on it, what happens next?"
The game is scheduled for August 5.