The Financial Times said the move for new funding comes two months after Turquoise was launched as an alternative to Europe's established trading systems.
Founded with support from banks including BNP Paribas, Credit Suisse, Morgan Stanley, Goldman Sachs and UBS, the platform had a market making agreement that guaranteed it a certain level of liquidity. However, that agreement expires in March.
Turquoise chief executive Eli Lederman confirmed to the publication that it is in talks with "potential strategic investors". He said the move would help ensure the "continued development" of the platform.
In addition, Turquoise is launching an equity incentive scheme that will allow its existing members to earn equity based on their trading levels.
Since its launch, Turquoise claims to have carved out a five per cent market share in the 13 European equities markets in which it operates.