* Graphic: World FX rates in 2018 http://tmsnrt.rs/2egbfVh
* Graphic: Trade-weighted sterling since Brexit vote http://tmsnrt.rs/2hwV9Hv (Addsa details, quotes, context)
LONDON, Feb 20 (Reuters) - Sterling rebounded against the dollar and jumped against the euro on Tuesday after a media report said the European Parliament would call for giving Britain "privileged" single market access.
The pound, which had been down 0.3 percent against the dollar at $1.3953 before the story was published by the Business Insider website, jumped to the day's high of $1.4015, up 0.2 percent. It later traded flat at $1.3993.
Against the euro, the pound rallied half a percent percent to 88.115 pence per euro. It had earlier changed hands at 88.495 pence per euro.
"We are starting to hear some of these small murmurs that things are moving towards a middle ground...a mutually beneficial Brexit," said Viraj Patel, London-based FX strategist at ING.
Speaking in Vienna on Tuesday, Britain's Brexit Minister, David Davis, said he was certain Britain and the European Union could reach a deal but urged the bloc to see securing an agreement as a "mutual endeavour".
According to Business Insider, the European Parliament is preparing to call for a more flexible approach in future relationship talks with Britain, a break from the position put forward by chief EU negotiator Michel Barnier.
Britain, which is due to leave the EU next year, says it will agree a transition deal with the EU by end-March.
Barnier said earlier this month that a transition deal was "not a given", suggesting the two sides remained far apart.
The EU leaders summit in late March is set to prove crucial for the progress of Brexit negotiations.
Patel said the pound was trading in a "new Brexit trading environment", rising on the back of positive surprises more than falling when talks seemed very strained, as they did last year.
Growing expectations that the Bank of England is at the start of a long interest rate hiking cycle also mean that the pound is increasingly impacted by other factors than Brexit talks.
Traders are looking to crucial British earnings data due later this week that could help cement bets the central bank will hike rates in May.
BoE Governor Mark Carney this month said rates needed to rise a bit faster and more than previously expected, and the market now prices in a roughly 80 percent chance of a May hike.
"We would need to see a significant negative 1/8earnings data 3/8 miss to see the market reprice the chances of a May hike," said Morten Helt, strategist at Danske Bank in Copenhagan, referring to data due on Wednesday.
Carney is due to speak to a British parliamentary committee on Tuesday, but analysts said they expected him to stick to the line given earlier this month. (Reporting by Tommy Wilkes; Editing by Jemima Kelly and Angus MacSwan)