PARIS/MILAN, Nov 21 (Reuters) - Amundi is considering offering UniCredit better terms to be able to extend a distribution accord that ties the French asset manager to the Italian bank and its biggest foreign market, a person close to the matter said.

Renewing the agreement would protect Europe's largest fund manager's foothold in a market that accounts for nearly a fifth of its assets under management (AUM) outside France.

Analysts have flagged concerns at the impact on inflows from the possible loss of the contract Amundi has with its main distributor in Italy, where its AUM amount to 197 billion euros ($215 billion), or 10% of its total.

Improvements could include giving UniCredit a bigger slice of the fees earned on the sale of products, the person, who declined to be named as discussions are private, told Reuters.

Amundi declined to comment. A spokesperson for UniCredit declined to comment.

Relations between the two partners have soured since Andrea Orcel tried in vain to renegotiate the terms of the accord after taking over as UniCredit CEO in 2021, several sources have previously said.

Amundi signed a 10-year distribution accord in 2017 when it bought UniCredit's Pioneer Investments for 3.6 billion euros.

Complicating matters, Amundi's main shareholder Credit Agricole last year became the single biggest investor in Banco BPM, an Italian mid-sized bank for which UniCredit was at one point close to launching a takeover offer.

Credit Agricole CEO Philippe Brassac told reporters this month it was no secret UniCredit was looking at ways "to optimise" the accord with Amundi.

"With partners things are always difficult because there are always demands, but it's a partnership that works well and in which we will find an equilibrium ... which suits both sides," Brassac, who also chairs Amundi, said.

Orcel, sources have said, is unhappy with the amount of Amundi funds the accord binds UniCredit to place with customers.

Amundi has to account for 80% of UniCredit's overall AUM in Italy, but penalties set by the contract for failing to meet that proportion become more punishing only below a lower 65-70% threshold, two people close to the matter said separately.

To grow UniCredit's fee income, Orcel set up an internal team which repackages funds supplied by global players under the bank's own 'onemarkets' label.

Meanwhile, Italian asset manager Azimut is building an Irish business that will produce and sell funds to UniCredit clients and will eventually become part of the bank.

UniCredit had 134 billion euros in AUM from fund and portfolio management as of Sept. 30.

Orcel has not ruled out ending the contract with Amundi, but a person with knowledge of the matter told Reuters he is happy to retain a partner that ranks among the top 10 asset manager globally and provides good support to the bank's sales network.

If the contract is to be extended, Orcel would like to agree on improved terms in the course of 2024, the person added.

If their relationship ended after 2027, it would still take UniCredit time to replace Amundi funds with other products.

To grow the fees UniCredit retains on the sale of funds to clients by making room for more profitable products, Orcel said last month it was "rebalancing" slightly its relationship with Amundi and would continue do to so.

In Italy, where distribution plays a key role in the fund industry, banks pocket at least 60% of the fees, a percentage that surpasses 80% when the lender owns the asset manager or there are multi-year accords in place. ($1 = 0.9168 euros) (Reporting by Valentina Za in Milan and Mathieu Rosemain in Paris; Additional reporting by Silvia Aloisi in Paris; Editing by Alexander Smith)