“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,” said Ryan spokeswoman AshLee Strong.

On Wednesday, former House Speaker John Boehner told a conference of futures trading executives that Ryan should be the nominee if no one was selected on the first ballot at the convention.

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But Ryan's arm can be twisted. Last year, after saying he didn't want the job, Ryan was eventually convinced to replace Boehner as speaker.

While Donald Trump has led many of the nation’s primaries so far, he does not have all of the delegates needed to clinch the nomination. A contested convention could happen if no candidate reaches the number of delegates needed.

CNN reports Trump and Cruz have warned there could be dire consequences if the GOP has a brokered convention, with Trump going so far as to claim there could be "riots."