* Yields rise on Trump, stimulus optimism

* Bond yields expected to remain depressed given uncertainty

* Three-month euribor rate drops to record low

* Euro zone periphery govt bond yields http://tmsnrt.rs/2ii2Bqr

LONDON, Oct 5 (Reuters) - Euro zone bond yields rose on Monday, with signs that U.S. President Donald Trump's health was improving and hopes for a stimulus agreement boosting risk appetite across markets.

Although Trump's health status remained unclear, there was some optimism after his medical team told reporters on Sunday he might return to the White House as early as Monday.

Signs of progress on coronavirus relief legislation in the United States also supported markets on both sides of the Atlantic.

The 10-year German bond yield was last up 3 basis points (bps) to -0.51%, still near recent lows at -0.552%.

Italian yields were up 1 bp to 0.76% after hitting a new record low at 0.72% in earlier trade.

But expectations for more European Central Bank stimulus before the end of the year and data on Friday showing euro zone inflation sinking deeper into negative territory are keeping euro zone bond yields near their recent lows.

Worries around a second wave of coronavirus infections remained in focus after the French government announced new restrictions, including the closure of bars, in Paris to combat rising cases and other countries across Europe were weighing up more measures to stop the spread of the virus.

"Further upside in yields looks limited though with corona jitters around the White House and numerous European hotspots fostering the safety bid," Commerzbank rates strategist Rainer Guntermann told clients.

"Overall this argues for Bunds to remain stuck in their confined range below the -0.5% range while BTPs rally on."

The ECB's bond purchases slowed last week and the bank bought less Italian and Spanish government debt over the past two months as market pressure stayed low despite a resurgence in coronavirus cases, data showed.

But recent data signalling a slowing euro zone economic recovery has led some, like Morgan Stanley, to factor in additional ECB stimulus earlier than they previously thought.

"Recent data has disappointed, suggesting the rebound is already losing steam, especially in the services sector," Morgan Stanley economists told clients on Monday.

"With inflation holding well below target and signs that the recovery is slowing, we recently brought forward our ECB call and now expect a 400 billion euro PEPP [the ECB's pandemic emergency purchase programme] top up and extension until end-21 in December."

Elsewhere, the three-month euribor interbank rate fell to a new record low at -0.509% as excess liquidity continues to keep money market rates depressed.

(Reporting by Tommy Wilkes and Yoruk Bahceli; Editing by Alex Richardson and Mark Potter)