* Euro back at weakest since May 2017
* Trump says a deal with China could happen soon
* Dollar near its recent highs, enjoys safe haven demand
* New Zealand dollar rises on central bank comments
* Graphic: World FX rates in 2019 http://tmsnrt.rs/2egbfVh (Recasts, adds details, new quote)
LONDON, Sept 26 (Reuters) - The dollar rebounded and was headed towards its highest since 2017 on Thursday, while the euro dropped to a 28-month low, amid optimism over a trade deal between the United States and China.
Despite the opening of an impeachment inquiry into U.S. President Donald Trump this week and mixed signals on a trade deal, the dollar has remained resilient. It has been in demand both when investors get nervous, and also when a deal with China - and a boost to the global economy - seems within reach.
The euro, by contrast, slipped to $1.0922, touching a 28-month low and eclipsing its lows of earlier this month, when talk of more European Central Bank monetary policy easing peaked.
While the Federal Reserve is cutting interest rates, other currencies do not look more appealing than the dollar, because of the cloudy outlook for the global economy and stop-start trade negotiations, said Neil Mellor, a markets analyst at BNY Mellon.
"You have a parade of ugly currencies. It's not obvious what else you buy instead," he said.
The dollar index, which measures it against a basket of other currencies, was last up 0.1% at 99.107, its strongest since it reached 99.37 earlier this month, the highest since May 2017.
Trump stoked hopes for a trade deal by telling reporters in New York that the United States and China were having "good conversations" and that an agreement "could happen sooner than you think".
Not everyone thinks the dollar will reign supreme, however.
"USD rallied on the back of growth weakening in the rest of the world economies, which export capital mostly into the U.S. A trade deal may allow global trade to rebound temporarily, helping growth in manufacturing economies, easing their capital exports and thus weakening the USD," Morgan Stanley strategists said in a note.
The biggest mover among the major currencies was the New Zealand dollar, which gained after its central bank governor said it was unlikely he would need to use unconventional monetary policy. The kiwi was last up 0.6% at $0.6299.
The trade-sensitive Australian dollar rose 0.2% to $0.6760.
China's yuan was up at 7.1270 per dollar in the offshore market.
The Japanese yen, perceived as a safe haven, rose 0.2% to 107.59 yen per dollar.
Sterling dropped 0.1% to $1.2336 after plunging more than 1% on Wednesday as conflict over Brexit gripped the British parliament.
(Editing by Larry King)