* Premafin not allowed to talk to funds about offer
* Creditor banks support Unipol
* Premafin owner fully behind Unipol - source (Adds detail, background)
MILAN, March 1 (Reuters) - Italy's Premafin, the holding company that controls troubled insurer Fondiaria-SAI, said on Thursday it was unable to make a decision on a bid from two private equity funds because its hands were tied by an earlier agreement with peer Unipol.
Premafin said in a statement that the exclusive nature of its agreement with Unipol meant it was not allowed to enter talks with another party, essentially sounding a death knell for the offer.
Bologna-based Unipol agreed in January to a 1.8 billion euro ($2.40 billion) deal brokered by Italian investment house Mediobanca to save loss-making Fondiaria.
That plan was challenged by a competing bid from private equity funds Palladio Finanziaria - a regional player with clout in Italy's North-East - and Sator, founded by Italian turnaround banker Matteo Arpe.
Premafin said the position of its creditor banks also made it impossible to make any decision on the offer. Italian banks Mediobanca and UniCredit, which are owed more than 180 million euros by Premafin and have a key say on Fondiaria's future, have already signalled they back Unipol.
The agreement with Unipol did not contain any penalties should the exclusivity clause be breached, Premafin said.
On Wednesday, a source said the Ligresti family, which controls Premafin, was fully behind Unipol's plan.
A takeover by Unipol, Italy's No.3 insurer by premiums, would create a company with 32 percent of Italy's non-life insurance sector and 37 percent of its motor insurance business that is able to compete with larger rival Generali.
The two funds, whose offer expires on March 8, have acquired 8 percent of Fondiaria and are ready to pump 450 million euros into parent Premafin.
Unlike the Unipol offer, which envisages three capital increases and a four-way merger, the offer by Palladio and Sator does not involve a merger.
Premafin said further meetings with the creditor banks about restructuring debt were scheduled in coming days. ($1 = 0.7501 euros) (Reporting By Stephen Jewkes; editing by Andre Grenon)