However, he said the matter fell under the purview of the Lok Sabha.
On December 28, Yadav had given notice under Rule 187 alleging that the Congress President had "intentionally, maliciously and disrespectfully twisted" the name of Leader of the House and Finance Minister Arun Jaitley in a tweet.
Gandhi, a Lok Sabha member, had tweeted in connection with Jaitley's statement after an agreement to end an impasse in the Upper House was reached between the treasury and opposition benches over Prime Minister Narendra Modi's remarks against his predecessor Manmohan Singh during the Gujarat assembly election campaign.
During the Zero Hour on the last day of the Winter Session, Yadav wanted to know the fate of his privilege notice, to which Naidu said it was under his consideration.
"Your notice is under my consideration. I have already told you, I will be taking action immediately, but it's not within the purview of Rajya Sabha, finally, it has to go to Lok Sabha. I will take a necessary decision at the earliest," the Chairman said.
The House was adjourned sine die later in the day.
Earlier, Naidu asked ministers to take prior permission along with reasons from the Chair for allowing their colleagues to lay papers in the House on their behalf.
He also remarked that when Parliament is in session, ministers should give "priority to Parliament".