The Financial Times is reporting that Clearstream is set to reject rival takeover bids from Deutsche Borse and Euroclear as too low.
The FT quotes the Cedel consortium - a part-owner of Clearstream alongside Deutsche Borse - as saying that the bids "were disappointing and further work will be needed".
Clearstream is understood to be open to offers in the region of $3 billion.
Euroclear is quoted by the FT as indicating that it might be prepared to extend its all-share offer.
The battle for control of Clearstream is seen as crucial to deciding the future of clearing and settlement in the European financial markets.