* Revised accord would help fee income at UniCredit

* Net fees gain prominence as interest rate boost wanes

* UniCredit is Amundi's main partner in its biggest foreign market

MILAN, Feb 20 (Reuters) - UniCredit wants to agree in 2024 improved terms for selling Amundi's funds to its clients, if the French asset manager is to retain its main Italian distributor after their contract runs out in 2027, a person close to the matter said.

Securing better terms would help UniCredit tackle the challenge banks face as interest rates peak: growing more stable fee income to offset the waning boost from higher rates.

An early renegotiation to see the contract extended on terms which are more favourable for UniCredit would allow the bank to add to its fees already from next year, the person said.

Banks benefit more from such contracts if the portion of fees on the sale of funds they retain is higher. Sources had previously told Reuters UniCredit also regarded contractual minimums with Amundi as too high.

Representatives for both Amundi and UniCredit declined to comment.

CEO Andrea Orcel, UBS' former investment banking chief, has a goal of bringing Italy's No.2 bank to eventually generate an additional 1.4 billion euros in fees a year.

To retain a key partner in its biggest foreign market, Amundi would consider offering UniCredit better terms, including a bigger slice of fees, sources have previously told Reuters.

The terms of the 10-year accord reflect those of the sale of the Pioneer Investments unit UniCredit clinched with Europe's biggest asset manager in 2017 to bolster its capital base.

Amundi paid 3.55 billion euros in cash, after Pioneer had paid UniCredit 315 million euros in extraordinary dividends.

When UniCredit presented yearly results this month, analysts asked if they should expect any delays to Orcel's strategy of bringing UniCredit to hold onto more of its asset management fees given that the Amundi contract ran until 2027.

Even if the accord ended, it would take time for UniCredit to gradually replace Amundi's funds in its clients' portfolios.

"We will see about our agreement with Amundi," Orcel said then.

"But I don't think it's an all or nothing between now and 2027," he said, adding it would be a progression "with 2027, obviously, being an important year as one of our key agreements is up for renegotiation."

UniCredit relies on Amundi for between 70% and 80% of its asset management business, Orcel said, adding the bank had been focusing on "creating value" on the portion "that is, in inverted commas, free".

Sources have said relations between the two groups were complicated by a decision in 2022 by Amundi's main shareholder, Credit Agricole to become the biggest investor in Banco BPM, a smaller peer which UniCredit has considered taking over.

Credit Agricole CEO Philippe Brassac expressed confidence in November the two partners would find "an equilibrium ... which suits both sides."

Under his fee drive, Orcel has set up an internal team which repackages funds supplied by global players under UniCredit's own "onemarkets" label.

UniCredit is also set to start distributing to its customers this year funds provided by Azimut under a partnership Orcel struck in December 2022 with the Italian asset manager.

Fees accounted for 32% of UniCredit 2023 revenue, up 1% year-on-year when excluding a 235 million euro hit due to reduced current account fees and the cost of securitisation deals. (Reporting by Valentina Za; editing by David Evans)