* Dollar tracks toward highest weekly close vs yen since May

* Pound gains as Johnson firms in polls

* Other majors mostly rangebound, awaiting trade news

* Graphic: World FX rates in 2019 http://tmsnrt.rs/2egbfVh

By Tom Westbrook

SINGAPORE, Nov 29 (Reuters) - The dollar headed for its highest weekly finish against the safe-haven yen since May on Friday, as data showing the U.S. economy on a firm footing prompted investors to scale back rate-cut bets.

Nerves persisted though, as other major currencies spent the week rangebound, navigating a blizzard of trade-war headlines that offered few clues as to when or how an overdue truce might be agreed between Washington and Beijing.

"There seems to be pretty good optimism around the trade talks going on between U.S. and China," said William O'Loughlin, a portfolio manager at Rivkin Securities in Sydney.

"Though as we know that can change on a dime...the rally doesn't feel like a euphoric, super-bullish rally, it does feel like climbing the wall of worry."

On Friday, the dollar was steady at 109.51 Japanese yen , and if it holds there will post a 0.7% gain for the week and hit its highest weekly close since May 31. Overnight trade was light with U.S. desks closed for Thanksgiving.

The British pound has been the week's other main beneficiary, adding half a percentage point as Prime Minister Boris Johnson's Conservative Party has firmed in opinion polls ahead of the Dec. 12 election.

Sterling was steady on Friday at $1.2910, while the euro held at $1.1012.

"The market has come to the view that this is Johnson's election to lose now," said Chris Weston, head of research at Melbourne brokerage Pepperstone, with expectations he can win with a large margin.

"That said, should any polls call this margin into question, where invariably there will be one or two, then GBP could see a sharp sell-off, although I would be using that weakness to buy."

The dollar's strength this week has drawn on hopes that the United States and China are indeed in the process of negotiating a ceasefire in their damaging tariff war, and strong U.S. economic data.

China has vowed to impose "firm countermeasures" after Trump's approval of a bill backing Hong Kong's pro-democracy protesters on Wednesday, but is yet to indicate whether they would have any bearing on trade talks.

U.S. growth picked up slightly in the third quarter, data showed on Wednesday, in contrast to other indicators showing a slowdown in global activity.

The Fed also flagged an upbeat outlook amid signs of labour market strength and a possible turnaround in business investment.