It has been reported that Alphyra originally planned to list on the London and Dublin stock markets but abandoned the idea in favour of a trade sale.
In August the company brought in NCB, Goldman Sachs and Citigroup as advisers, leading to speculation that a deal for a sale was being prepared.
Benchmark owns around 67 per cent of Alphyra – which develops secure web payment systems – and could make €400m (£278m) if a deal materialises. Benchmark paid €88m for its buyout of the firm in 2003.
Benchmark typically invests between $3m and $5m, although its stated investment range is $100,000 to $15m (£8.5m). The firm specialises in the technology sector and has stakes in companies such as videogame developer Codemasters.
The company also has a stake in Spanish firm Setanta, which along with Benchmark has been linked to a bid for live broadcast rights for Premiership football.
Powerscourt director Victoria Palmer-Moore leads the account.