* Bid starts on Tuesday

* Creval shares trading above offer's 10.5 euro price

* Creval says fair price range between 12.95-22.7 euros

* Creval says merger has valid rationale

MILAN, March 29 (Reuters) - Italian regional bank Creval on Monday said a takeover offer by Credit Agricole Italia (CAI) was a good strategic move, but the price should be at least 23% higher.

The Italian arm of Credit Agricole in November said it would spend 737 million euros ($868 million) to expand its presence in Italy's consolidating banking sector - its biggest market outside France.

CAI is offering 10.50 euros a share to buy out Creval investors. But the Italian lender said a fair price would be between 12.95 and 22.7 euros, based on analyses by advisers Bank of America and Mediobanca.

"CAI's project has a sound strategic rationale, but it must take into account ... that Creval has undergone a transformation. It is a completely different and extremely solid bank," CEO Luigi Lovaglio told reporters.

Creval in 2018 raised 700 million euros in cash from investors - eight times its market value - to fund a restructuring that has cut problem loans and costs in preparation for an eventual tie-up.

Lovaglio, who made his name as head of Bank Pekao, the former Polish unit of UniCredit, said the bid had to reflect a number of factors, including Creval's high excess capital.

"Creval is extremely valuable, and those who know about banking are aware of it. It's a rare opportunity and (if I were CAI) I'd do everything possible to bring this home - 10.5 euros isn't adequate," Lovaglio said when asked if he expected the price to be raised.

Creval shareholders representing around 20% of the its capital have already rejected the offer as too low.

With its roots in Lombardy's Valtellina area, Creval would double CAI's market share in Italy's wealthiest region.

Shares in Creval have consistently traded above the bid's price. At 1326 GMT Creval shares were up 0.8% at 12.11 euros.

CAI first invested in Creval in 2018, when the two lenders struck an insurance partnership. CAI has said it will keep its Creval stake, which is set to reach 18%, even if the takeover fails.

The offer runs from Tuesday to April 21, following approval from banking supervisors and market regulator Consob.

Creval estimates the merged entity would reap a net 321 million euro boost from Italian rules aimed at spurring corporate mergers in 2021. But CAI said last week it did not know whether such incentives could be tapped.

Creval also said integration and restructuring costs projected by CAI at 345 million euros were too high compared with the average in recent banking mergers in Italy.

"There are no plans for job cuts and we're happy about that, but we'd also be happy to know how the money would be spent," Lovaglio said.

($1 = 0.8490 euros) (Editing by Valentina Za, Edmund Blair and Barbara Lewis)