Mr Sunak tweeted a picture of himself working at his desk with the caption: "Cracking on with preparations for my first Budget on March 11.
"It will deliver on the promises we made to the British people – levelling up and unleashing the country’s potential."
Mr Shapps said on Sunday: "I haven’t heard whether the date of March is confirmed as yet.
"He is probably looking at it."
Mr Sunak replaced Sajid Javid as the Chancellor last week following a Cabinet reshuffle.
Mr Javid was reportedly unhappy with requests made by the prime minister to dismiss his team of special advisers.
The former Chancellor said he was left with "no option" but to resign.
During Boris Johnson's Cabinet reshuffle Mr Javid was asked to stay in post, but on the condition he "replaced all" his political advisers.
Speaking last week, former Chancellor Sajid Javid said 'any self-respecting minister' would reject Number 10's conditions
"I don't believe any self-respecting minister would accept such conditions," he said.
"Those were the conditions requested by the prime minister, that was of course his prerogative".
It had been reported those conditions were being imposed by Boris Johnson's top aide Dominic Cummings, but Mr Javid said the demands were made by the prime minister himself.