reports.
His campaign to be the next Prime Minister, not yet formally announced, will be "very conciliatory" and "united based", it is said.
If he throws his hat in the ring as expected he will be up against Mr Sunak, who this morning officially revealed he is running.
The pair last night held talks in an attempt to strike some kind of deal but seemingly failed to come up with a pact.
It means they will likely go head-to-head in a battle for the Tory crown, alongside third-placed Penny Mordaunt - whom Boris today unsuccessfully urged to drop out and get behind him.
All three candidates have backing from a series of big hitters, with Mr Sunak the frontrunner.
The ex-Chancellor, who today promised to fix Britain's broken economy, is storming ahead in the contest with support from 148 named MPs - easily enough to land him a spot in the final.
Mr Johnson follows with 60, while Ms Mordaunt trails in the back with 25.
Among those behind Mr Sunak is Suella Braverman, who today said he is the only person that fits the bill for PM.
Writing in , she said that while it was "an honour" to serve in Boris' Cabinet, now isn't the time for "fantasies".
Kemi Badenoch, Lord David Frost and David Davis are also on his side.
On the opposing team, Mr Johnson counts Jacob Rees-Mogg, Ben Wallace and Nadhim Zahawi among his core supporters.
It comes as...
The once-close duo spent last night several hundred feet apart refining their campaigns.
Boris, who hours earlier jetted back from his Caribbean holiday and headed straight to his London HQ, hit the phones in Westminster to try to get those wavering onside.
But over in Parliament, his rival was hammering away to get them on team Rishi.
They then united to hold a not-so-secret meeting to try to put aside their differences and heal the party's rifts.
Allies said they could have formed a partnership, with Boris in the chair and Rishi as his deputy.
But Mr Sunak's low-key tweet announcing he wants to be the new Conservative Leader suggests the conversation didn't go to plan.
In it, he vowed to "deliver for our country" - without the aid of slick graphics or a fancy video montage.
Ms Mordaunt, who has held Cabinet posts including defence secretary and came third in the race to replace Boris in the first leadership race, announced her bid on Friday.
Mr Johnson has not yet done so but plans to tomorrow as he now has the required 100 supporters, according to ally Chris Heaton-Harris.