* Impeachment risk recedes, Trump stokes trade-deal optimism
* Dollar hands back some gains to trade-exposed currencies
* Sterling nurses losses as Brexit outlook clouds
* Graphic: World FX rates in 2019 http://tmsnrt.rs/2egbfVh
SINGAPORE, Sept 26 (Reuters) - The dollar consolidated on Thursday, staying near multi-week highs against most major currencies while slipping against riskier ones after U.S. President Donald Trump said there could be a trade deal with China soon.
"It's the Trump pump, and it works," said Matt Simpson, senior market analyst at Gain Capital in Singapore.
"But there's not really any major moves either, it's a slight boost to risk," he said, noting traders were also trying to assess the likely direction of a Trump impeachment probe opened by the Democrats on Wednesday.
The Australian dollar edged higher and the safe-haven yen was marginally firmer at 107.65 per greenback, not far from a one-week low.
The euro bounced from an overnight two-week low but remained under $1.10 at $1.0959. Sterling also edged off a two-week low hit as investors priced in many more months of Brexit and election risk, touching $1.2368 on Thursday.
Trump stoked hopes for a trade deal by telling reporters in New York that the U.S. and China were having "good conversations" and that an agreement "could happen sooner than you think".
That helped the Australian dollar claw 0.2% higher, while the New Zealand dollar kicked ahead further after New Zealand's central bank governor said it was unlikely he'd need to use unconventional monetary policy.
The kiwi rose 0.6% for the day to $0.6307. The Chinese yuan was slightly firmer at 7.1229 per dollar.
The dollar index nudged lower to 98.877 after its sharpest rally in three months overnight. It remained stronger than at any point last week.
The greenback had at first been sold when U.S. House of Representatives Speaker Nancy Pelosi said the Democratic-led chamber was launching an impeachment inquiry over Trump's handling of a call to Ukrainian President Volodymyr Zelenskiy.
A summary of the call subsequently released by the administration showed Trump pressed Zelenskiy to investigate former Vice President Joe Biden - Trump's leading Democratic rival - but did not show Trump threatening to withhold aid.
The House inquiry could trigger a trial in the Senate on whether to remove Trump from office, though that is seen as unlikely to succeed because Republicans control the Senate.
"Markets shrug these things off very, very quickly and we move on to the next stuff," said Nick Twidale co-founder of Sydney-based trade finance provider Xchainge, who said investors were shifting the prospect of impeachment to the long-term.
"As it moves on, it's going to be interesting, but we have to go back to the fundamentals and fundamentals are going to push the dollar higher over time." ( Editing by Richard Borsuk)