* Chairman designate, board to look for new CEO

* Mustier says his strategy no longer in line with board's

* Mustier ruled out M&A, Rome looking for Monte Paschi buyer

* Mustier cleaned up UniCredit, bolstered capital

MILAN, Dec 1 (Reuters) - Italy's UniCredit said Chief Executive Jean Pierre Mustier will step down in April next year after clashing with the bank's board over strategy.

The French former investment banker has steered UniCredit through a painful restructuring in the past four years, bolstering its balance sheet and cutting exposure to debt-laden Italy.

After fruitless attempts at a cross-border deal, Mustier, 59, had ruled out mergers and acquisitions, a stance increasingly at odds with the consolidation fever sweeping Italy's fragmented banking sector.

"Over the last few months, it has become apparent that the Team 23 (business plan's) strategy and its core pillars no longer corresponds to the board's current thinking," Mustier said in a statement late on Monday.

"Hence I have decided to retire from the group at the end of my mandate in April 2021, to allow the new board to elaborate a future strategy."

Shares in UniCredit closed down 5% on Monday, hit by concerns about leadership. By contrast, shares in state-owned Monte dei Paschi (MPS) surged 3%.

The government is looking for a buyer for the Tuscan bank it rescued in 2017 and sources have said it had identified UniCredit as the ideal partner due to its robust balance sheet.

Reluctant to take on the loss-making lender for years at the fore of Italy's banking crisis, Mustier had set strict terms for a deal in negotiations with Rome, the sources had said.

News of Mustier's departure is seen easing a potential tie-up, after UniCredit named as chairman elect Pier Carlo Padoan, the former Italian economy minister who oversaw MPS' bailout.

UniCredit said Padoan and the board would now look for a CEO replacement, both inside and outside the bank.

Head hunter Spencer Stuart is helping with the selection process. The Italian press has listed among potential candidates Mediobanca CEO Alberto Nagel and former MPS chief Marco Morelli, as well as UniCredit director Diego De Giorgi, the bank's co-chief operating officer Carlo Vivaldi and Francesco Giordano, co-CEO of commercial banking for western Europe.

Poste Italiane on Monday dismissed rumors CEO Matteo Del Fante could be a candidate.

UniCredit is the latest major European bank to announce a CEO departure this year, with Credit Suisse, UBS, ING, Commerzbank and Lloyds all making leadership changes.

The pandemic has compounded the existential challenge faced by European banks due to negative interest rates that make lending unprofitable, competition from larger U.S. and Asian rivals, and tech giants expanding into finance.

Mustier had argued mergers "were no panacea" despite regulatory calls to cut costs through tie-ups to offset shrinking revenues.

People familiar with the matter said he faced increasing discontent over his failure to lift the share price and lack of a clear strategy, after a pandemic-driven dividend ban derailed plans to return more cash to shareholders.

UniCredit trades at a 66% discount to its book value, versus 45% for rival heavyweight Intesa Sanpaolo.

Piling pressure on Mustier, Intesa this summer overtook it as Italy's No. 1 bank by snapping up peer UBI in a surprise move that triggered a chain-reaction.

Credit Agricole last week announced a buyout offer for third-tier Italian lender Creval while Banco BPM, which had held preliminary merger contacts with UniCredit, has welcomed merger overtures from the top investor in BPER Banca. ($1 = 0.8351 euros)

(Editing by Tom Brown and Louise Heavens)