Twelve top managers at Swiss private bank Sarasin
The Tagesanzeiger newspaper said, without sourcing, that the letter was written by practically the whole top level of management at Sarasin, meaning the bank would likely see an exodus of top staff if Baer were to take over.
A spokesman for Sarasin declined to comment on the report.
Sarasin, one of a host of smaller private banks in Switzerland, said last month Rabobank was looking at all options for the 46 percent of Sarasin it owns, which corresponds to 68 percent of voting rights.
Sarasin's management has previously said it hoped Dutch Rabobank will make a decision this month about its controlling stake that allows the bank to remain independent.
Swiss newspapers have said Julius Baer
In an interview with Swiss newspaper Le Temps Julius Baer Chief Executive Boris Collardi said a takeover of Sarasin would create synergies.
But Collardi said it would make no sense for Baer to buy the remainder of Rabobank's stake, if Raiffeisen were to make an offer for 33 percent of the voting rights.
The Tagesanzeiger paper said Baer was reportedly offering 39 Swiss francs per share, which would value Sarasin at about 2.5 billion Swiss francs (1.72 billion pounds).
Julius Baer spokesman Jan Vonder Muehl declined to comment.
Sarasin's shares closed at 34.50 Swiss francs on Friday, giving the bank a market capitalisation of 1.78 billion Swiss francs based on 51.6 million shares outstanding.
The Swiss private banking industry is seen in dire need of consolidation given rising costs and falling revenues, particularly as the industry has been forced to move away from a business model that often relied on offshore tax evasion. ($1 = 0.916 Swiss Francs)
(Reporting by Caroline Copley)