The report in The Telegraph newspaper - which came two days before British Prime Minister Theresa May is due to make a key speech in Italy on Brexit - said close friends of Johnson believed he would have no choice but to walk away if May advocates permanently paying for access to the European Union's single market.

That prompted a half-cent jump in the pound, to $1.3535 from around $1.3485 before the article was published.

British bookmaker Ladbroke's said on Twitter that they were offering 11/4 odds, reflecting a more than 73 percent chance, of Johnson either quitting or being sacked by next Monday.

"Markets seem to be thinking that (Boris resigning) would leave (Prime Minister) Theresa May with a freer hand to push through a softer Brexit," said Richard Wiltshire, chief foreign exchange dealer at ETX Capital in London, which he said would be a "positive" for sterling.

But when questioned about the Telegraph report, Johnson said he was not going to resign, that the government was "working together" and that it would "deliver a fantastic Brexit". [nL5N1M043S]

May later said Johnson was "doing good work" and should not be sacked, according to a tweet by a Sky News reporter. [nL5N1M055T]

By 1550 GMT sterling was trading up 0.1 percent on the day at $1.3511.

It had been pressured earlier as traders digested comments made on Monday by Bank of England Governor Mark Carney.

"After the recent strong run it's probably ready for a bit of a consolidatory phase," said Martin Arnold, currency strategist at ETF Securities.

Sterling rose as much as 3.3 percent last week, jumping more than four cents to $1.3618 on the back of hawkish messages from the BoE and Gertjan Vlieghe, one of the Bank's rate-setters normally considered a dove. The currency is up nearly 19 percent against the dollar this year.

But it slid off its highest level since the Brexit result after Carney made comments on Monday that some analysts said were aimed at managing market expectations of the pace and number of rate hikes from the British central bank.

Key events for sterling traders this week apart from May's Brexit speech will be a reading of UK retail sales on Wednesday and ratings firm Moody's UK sovereign debt rating also due on Friday.

(Reporting by Jemima Kelly and Ritvik Carvalho; Editing by Abhinav Ramnarayan, Greg Mahlich)

By Ritvik Carvalho and Jemima Kelly