Saraki said this on Tuesday night while speaking with State House correspondents after a closed-door meeting with President Muhammadu Buhari in Abuja.
Buhari met with the leadership and principal officers of the National Assembly as part of efforts to resolve the 2016 Budget impasse.
Saraki said the lawmakers came to inform the President and his team of the solutions they had found to the budget impasse.
He said both sides agreed on the way forward and assured Nigerians that the process would be completed in a matter of days.
He said: “We just finished a meeting with the President and the Vice President.
“We came to let them know some of the solutions that we found in moving the budget process forward and we are happy to say that we have agreed on the way forward.
“We believe that this process will be completed in a matter of days rather than weeks.
“So, it is good to Nigerians and all of us, we have found a way forward and in a matter of days, the budget will be ready for the President’s assent.”
Saraki also said committees had been set up on both sides to hasten actions on the process.
He said the committees would meet over the next few days to “tidy up a few loose ends and here and there and the outcome will be satisfactory to everybody”.
Also commenting on the outcome of the meeting, the Minister of Budget and National Planning, Udoma Udo Udoma, confirmed that the Executive had agreed with the Legislature to resolve all grey areas in the budget and the modalities of doing so in the next few days.
Udoma said: “We have agreed to work together to resolve all issues in the next few days and we have also agreed on the modalities of or doing so.
“It was a very good meeting and it was very positive.
“Within the next few days, all issues will be resolved.
“We are working together, both the Executive and the Legislature, to sort those things out.
“Within the next days, all matters will be resolved.”
Those who attended the meeting included Vice President Yemi Osinbajo; Saraki; the Speaker of the House of Representatives, Rt. Hon. Yakubu Dogara; the Deputy President of the Senate, Ike Ekweremadu; and the Deputy Speaker of the House of Representatives, Hon. Yusuf Lasun.
Others were the Senate Minority Leader, Godswill Akpabio; and the House Leader, Femi Gbajabiamila, among other leaders of the National Assembly; the Chief of Staff to the President, Abba Kyari; and Udoma.
The Senior Special Assistant on National Assembly Matters (Senate), Ita Enang; and the Senior Special Assistant on National Assembly Matters (House of Representatives), Samaila Kawu, also attended the meeting