These leaders included Rajnath Singh, Piyush Goyal, Arjun Ram Meghwal, Prakash Javadekar, Smriti Irani, Gajendra Singh Shekhawat and Rajyavardhan Singh Rathore.
Principal Secretary to Prime Minister Nripendra Misra and Additional Principal Secretary P.K. Mishra also visited Shah's residence.
Rajnath Singh also met Prime Minister Narendra Modi.
Meanwhile, Modi visited Union Finance Minister Arun Jaitley at his residence, hours after he opted out of the Union Cabinet citing health conditions.
The meeting came against the backdrop of the letter written by Jaitley to Modi earlier in the day asking him not to include him in the new cabinet, citing health issues.
Modi inquired about Jaitley's health during the meeting. Jaitley has been a key leader of the government, one of its most articulate faces and a key trouble shooter.
In his letter, Jaitley had said: "During the last 18 months, I have had some serious health challenges. My doctors have enabled me to emerge out of most of them."
"I am writing to you formally to request you that I should be allowed a reasonable time to myself, my treatment and my health and therefore not be a part of any responsibility, for the present in the new government," he said.
Jaitley, who said he had already communicated his request to Modi before he left for Kedarnath, held that even though he was able to discharge the responsibilities assigned to him during the Lok Sabha election campaign, "I would in future, for some time, like to keep away from any responsibility. This will enable me to concentrate on my treatment and health."
Modi had submitted resignation of his council of ministers last week after the results of Lok Sabha elections. President Ram Nath Kovind had accepted the resignations and asked the Prime Minister to continue till the new government assumes office.
More than 20 leaders are likely to take oath along with Modi on Thursday.
( With inputs from IANS )