By Kevin Buckland

TOKYO, April 28 (Reuters) - Japan's Nikkei rose on Monday, putting it on course for a four-day winning streak, with auto-sector stocks among the top performers after Toyota Motor revealed that it may invest in key parts supplier Toyota Industries.

Sentiment was also buoyed broadly by some signs of a thaw in the Sino-U.S. trade standoff, with President Donald Trump saying on Friday that he had spoken with Chinese leader Xi Jinping.

Beijing has denied direct talks are underway, but has exempted some U.S. goods from steep levies.

The Nikkei .N225 was up 0.5% at 35,887.89, as of the midday trading recess. Earlier in the day, the index rose as high as 36,075,26, crossing the psychological 36,000 level for the first time since April 1.

The benchmark index hasn't posted a four-day winning streak since January.

The broader Topix .TOPX gained 1%.

Trump also said on Friday that a tariff agreement with Tokyo is very close, without providing details. Japan's top negotiator, economy minister Ryosei Akazawa, will be in Washington from Wednesday for a second round of talks.

"The backdrop to everything is U.S. tariff negotiations, and rising optimism there is supporting stock markets," said Maki Sawada, a strategist at Nomura.

However, ahead of a national holiday on Tuesday in Japan, and in a week packed with earnings reports that includes some of Wall Street's Magnificent Seven tech megacaps, "investors will be reluctant to chase the market much higher", Sawada said.

Transport equipment .ITEQP.T jumped 4.3%, making it the standout performer among the Tokyo Stock Exchange's 33 industry sectors.

Toyota Motor 7203.T climbed 5.5%. Over the weekend, Japan's biggest automaker said it was exploring the possibility of investing in a potential buyout of Toyota Industries 6201.T.

Shares of Toyota Industries were locked in a buying frenzy, remaining untraded due to excess demand and poised to surge the daily limit of 23% by market close.

Bloomberg News reported on Friday that Toyota Chairman Akio Toyoda and his founding family have proposed acquiring Toyota Industries in a potential 6 trillion yen ($41.75 billion) deal.

One notable decliner was chip-testing equipment maker Advantest 6857.T, a Nvidia supplier, which tumbled 5.4% after its profit forecast trailed analysts' estimates.

($1 = 143.7200 yen)

(Reporting by Kevin Buckland; Editing by Sherry Jacob-Phillips)

((Kevin.Buckland@thomsonreuters.com;))