The phrase "intention of asking" is correct and usable in written English.
You can use it to describe the purpose or goal of asking someone a question. For example, "He looked at me with the intention of asking for help."
He had come to Laos with the secret intention of asking Ms. Kubicka to marry him.
The city has no intention of asking that the keys to the city be returned.
[New York Post] David Berkowitz, the "Son of Sam" serial killer, said he has no intention of asking for parole.
"We have never had and do not have any intention of asking for the extradition of Mr Megrahi.
The mayor has no intention of asking his former campaign consultants to refrain from lobbying, said Edward Skyler, his spokesman.
"We have never had and don't have any intention of asking for the extradition of Mr Megrahi.
"I don't think the intention of Ask.fm is to be harmful," he says.
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The columnist had no intention of winning (asked what he would do if he did win, Buckley replied, "Demand a recount") but wanted to build a Conservative Party in New York that would discourage G.O.P. candidates from swinging too far left.
Whether because of Mr. Schomburg's influence or because managers simply had no intention of taking the extraordinary step of asking another agency to obtain images, Mr. Rocha's request soon found its way into a bureaucratic dead end.
The primary objective of this research was to test the unique and interactive effects of asking about future intention to get screened for CRC (either before the past CRC screening behavior question or not at all) and survey mode (mail versus telephone) on the accuracy of self-reported CRC screening behavior.
