The firm was tight-lipped about the potential deal and said in a very brief statement: "There can be no certainty that an offer will be made nor as to the terms on which any offer might be made."
The announcement was released in response to recent movement on its share price.
Bespak failed to return calls from Outsourcing-Pharma.com seeking comments on a potential deal.
The news comes just three months after the drug device maker announced it would cut up to 160 jobs at its Milton Keynes facility, where Exubera is produced.
The firm said that following the slow take-up by diabetics of the once-touted blockbuster, Nektar Therapeutics and Pfizer - the developers of Exubera - had to revise their short term forecasts for the inhalation device, which resulted in a reduction of production.
Exubera, the world's first powdered insulin product, is inhaled into the lungs before a meal, using a proprietary inhalation device made under contract on a 50:50 split by Bespak along with The Tech Group, a subsidiary of West Pharmaceuticals Services.
If Bespak confirms an acquisition deal, it could prove a lucrative move for the potential buyer.
In the financial year ending 28 April 2007, Bespak saw its operating profit jump 19 per cent to $17.8m (€12.6m).
In addition, sales rose 44 per cent to $126.5m during the period, a performance the company attributed partly to strong sales of the Exubera inhaler.
And despite the chequered future of the drug, the firm remains confident it shouldn't impact its financial situation as it has diversified its business and does not depend entirely on its contract with Pfizer.
The company has a portfolio of 15 projects - including the ones with Pfizer, Sanofi-Aventis and Boehringer Ingelheim - of which five were signed last year.
In other news , The Tech Group recently announced the opening of a new manufacturing Plant in Walker, Michigan.
With this expanded new facility, the contract manufacturer has invested $17.3m and created 200 jobs.
The Walker plant contains 37 injection molding machines and manufactures medical components and devices.