The meeting was held inside the Presidential Villa, Abuja.
The Federal Executive Council had on Wednesday approved the document, paving the way for Buhari to present it to the lawmakers.
The Minister of Budget, Udo Udoma, had told State House correspondents that it would be at the discretion of the National Assembly to decide when the budget would be presented after the President must have communicated his intention to them.
Saraki told reporters after the meeting with the President that the document would be presented within the next 10 days.
He expressed confidence that with the level of works that had gone into the preparations, the budget would be passed into law by the National Assembly earlier than that of previous ones.
He said, “We are ready, once the document comes to us, we are ready. I think this time round, a lot of work has taken place behind the scenes.
“There is a lot more collaboration and you will see the result of that in the timeframe it will take after the President will have presented it.”
When asked for details of the budget and when it would be presented to the National Assembly, Saraki said, “I have not seen the details until the President lays it before us. I am sure within the next 10 days, it will be presented.”
When asked if the issue about the Medium Term Expenditure Framework, which the Senate described as empty and returned to the Executive had been resolved, Saraki described the issue as “work in progress”.
“That is still work in progress. I am sure that very soon, that matter will be concluded. But I am very optimistic that this year’s budget will be passed much more sooner than what we saw in the past,” he said.
Udoma had replied the Senate on Wednesday, saying the MTEF, which the lawmakers rejected, was a well-prepared document which was produced after extensive consultations with the private sector and Non-Governmental Organisations.
Saraki also described the walkout staged by Peoples Democratic Party senators following the defection of their colleague to the All Progressives Congress as “democracy at work”.
“That was democracy at work. The opposition party has its views about the defection of a senator to the APC. Calm has been restored to the Senate and we are one family again,” he said.