The meeting explored all options to strengthen the party before the 2014 Parliament elections.
Singh said a formal decision on BSY would be taken at a BJP parliamentary board meeting but indicated the return of the Lingayat strongman was only a matter of time.
Every decision will be taken in the forum concerned and would be known soon, he said.
A senior BJP leader from Karnataka said: The return of Yeddyurappa to BJP is almost certain. It is going to be unconditional. And it would be in the interest of both the BJP and Yeddyurappa.
The responsibilities of the former chief minister would be decided by the central core committee of the BJP in a week.
Yeddyurappa had quit the BJP in April 2011 after he was removed as the chief minister by then party president Nitin Gadkari following charges of corruption.
He later formed the Karnakata Janata Paksha (KJP) ahead of the Assembly elections in the state.
In the last few months,however,the BJP and Yeddyurappa have been working to mend fences.
The KJP recently extended support to the BJP prime ministerial candidate Narendra Modi,with BSY saying: I am ready to extend unconditional support to the BJP-led NDA under the leadership of Modi.
At the Mumbai meeting Tuesday,Rajnath elicited views of Karnataka leaders.
Sources said,There is no real opposition to Yeddyurappa. A couple of leaders are worried he may again hijack the organisation,though.
They said the dissenting voices had been warned his staying outside was more damaging to the BJP.
The sources indicated Yeddyurappa was in direct talks with Modi and Singh,who said the party would have to take steps to consolidate and prevent division of votes to increase its tally in Lok Sabha.
A senior Karnataka leader said,We are all reconciled to Yeddyurappa re-joining the BJP. But central leaders will have to ensure smooth functioning. He should not dominate the party in Parliament polls.