"The speaker is grateful for the support, but he is not interested. He will not accept a nomination and believes our nominee should be someone who ran this year," Ryan spokeswoman AshLee Strong said.
Ryan has consistently said he does not want to be his party's nominee for president. But former House Speaker John Boehner told a conference of futures trading executives Wednesday
that Ryan should be the party's pick if no one was selected on the first ballot at the convention.
Ryan was also forced to beat back efforts to recruit him to run earlier this month.
However, Ryan ruled out running for speaker last year before being lobbied heavily by his colleagues and, ultimately, stepping forward as a consensus candidate to replace Boehner.
The GOP field is currently led by billionaire Donald Trump, who has dominated contests across the country and tallied 640 delegates out of the 1,237 needed to clinch the nomination. His closest competitor is Texas Sen. Ted Cruz, who has won 405 delegates.
A brokered or contested convention could occur if no one reaches the magic number.
Both Trump and Cruz warned fellow Republicans Wednesday of dire consequences if the GOP establishment attempts to have a brokered convention this summer.
"I think you'd have riots. I think you'd have riots," Trump said Wednesday on CNN's "New Day." "I'm representing a tremendous many, many millions of people."
Cruz said party leaders getting behind a brokered convention would be disastrous.
What is a 'brokered convention'? Here is a (kind of) simple explanation
"I think that would be an absolute disaster. I think the people would quite rightly revolt. The way to beat Donald Trump is at the ballot box," the Texas senator said on "New Day."
"If it ends up happening that we get to Cleveland and nobody has 1,237 delegates, that Donald has a whole bunch of delegates and I have a whole bunch of delegates and we come in neck and neck, then it is up to delegates to decide," he added.
Republican National Committee Communications Director Sean Spicer said Wednesday that a chance for a brokered convention still remains.