The bid is being put forward by Highland Star, an investment group led by Roddie Fleming, a member of one of Britain's wealthiest families, in conjunction with Wyfold International, a new private equity firm backed by Allen.
Allen's group is through to the second round of the auction, along with rival private equity firms Graphite Capital, Advent, 3i and one other unnamed group.
Kurt Geiger, which sells the Jimmy Choo, Gina, Marc Jacobs and Chloe brands, was put on the auction block last year by owners Barclays Private Equity.
If Allen is successful in his joint bid with Fleming, it would mark the former ITV boss's first big investment in the retail sector. It is also believed Wyfold International are eyeing other retail investment opportunities.
Allen has previously headed the catering division of Granada and started his career as an audit manager for British Steel.
Allen is currently making waves in the media industry, as chairman of Global Radio, with a bid for GCap.
Global Radio was launched last year when it bought the Chrysalis radio stations in a £170m deal.
However, the bid has not been openly welcomed after it emerged last week that GCap's major investors are refusing to meet Global until they hear chief executive Fru Hazlitt outline her new strategy for the company on February 11.
At the same time, press reports have linked Global with a bid for Virgin Radio.
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