Asked about his plans as he left his London home on Tuesday morning, Mr Portillo said: "No words today. You'll hear in the next couple of days."
Shadow foreign secretary Francis Maude would also not be drawn on whether he would be standing for the Tory leadership during an interview on BBC Radio 4's Today programme.
He said: "All of this will be made clear at a time of our own choosing."
Mr Portillo was defence secretary in John Major's last Conservative government, and shadow chancellor in William Hague's Conservative opposition.
He is the early and overwhelming favourite to take over the party after its second successive election defeat.
None of the other potential candidates has so far put their names forward, although Ann Widdecombe and Iain Duncan Smith have said they are considering standing.
The leadership election can begin officially only when parliament returns on Wednesday and Conservative MPs elect the new chairman of the party's 1922 committee which will oversee the contest.
'Think things through'
Mr Portillo spent the weekend in Morocco and returned to London on Monday.
He spent much of Monday in discussion with advisers, and the BBC understands that he has decided to stand for the leadership.
Former chancellor Kenneth Clarke denied on Monday that he had already agreed on a dream ticket deal with Mr Portillo.
"It is not true, as some of this morning's (Monday) newspapers say, that I have a pact with Michael Portillo or anybody else and I've had no negotiations about any such pact," the ex-chancellor said.
"I don't intend to make my mind up about exactly what I'm going to do for a week or two and I hope that other candidates in this situation will take the same view.
'Take stock and listen'
Earlier, a similar appeal was issued by shadow defence secretary Iain Duncan Smith: "I think it shows a degree of unseemly haste if people now suddenly say they know all the solutions to our problems and are able to wave a magic wand."
He said the party "does need to get itself into the 21st century" and "look more like" the country it wanted to govern.
Widely tipped as a leading rightwing contender, Mr Duncan Smith is thought likely to attract the support of former prime minister Lady Thatcher.
He has already been backed by former party chairman Lord Tebbit, who warned against the Conservatives selecting a leader who was pro-euro - like Mr Clarke.
The peer described Mr Duncan Smith, successor to his Commons seat, as a "normal, family man with children".
That could be an early warning sign of the campaign ahead for Mr Portillo, who has spoken of having homosexual experiences as a young man.
However, a Portillo campaign has been boosted by a poll suggesting he is favourite to succeed Mr Hague among Tory voters, with 34% supporting him compared to 21% for Mr Clarke.
When all voters were asked in the Daily Telegraph/ Gallup survey the position switches, with Mr Clarke attracting 31% and Mr Portillo 27%.
Miss Widdecombe, the survey suggests, is far behind both men with support from 15% of Tory voters and 10% of the total.
The shadow home secretary is planning to take soundings from MPs before announcing her plans.