The Dutch giant was in the running for Bass last year but was outbid by Interbrew.
It is now expected to make a play for the Burton-on-Trent based brewer.
Other contenders
Carlsberg-Tetley and South African Breweries were also linked last year with Bass - but are thought to be unwilling to swallow the entire Bass portfolio, as opposed to individual brands.
Mr Byers' predecessor Margaret Beckett blocked Bass's take-over of Carlsberg-Tetley in 1997 because it would have given the company too great a market share - a decision which led to Bass's decision to exit brewing altogether.
South African Breweries, which signalled its intention of making UK acquisitions by gaining a listing on the London Stock Exchange, would not have a problem with market share.
But it is widely expected to concentrate on profitable niche brands - such as its recently acquired Czech beer Pilsner Urquell - rather than making a play for the mass market with Bass.
US giant Anheuser-Busch, which owns the Budweiser brand and was last year linked with a possible take-over of Scottish and Newcastle, is also thought unlikely to be interested in the entire Bass business.
"Anheuser has been very successful at focusing on one brand. It is unlikely to risk buying a diverse portfolio like Bass," one drinks analyst says.
Heineken struggling
Heineken, on the other hand, is struggling in the UK market.
It has never had its own UK operation, relying on third parties to brew and distribute its core brand.
When Interbrew took over Whitbread last year, it took on the contract to distribute Heineken, which, in the view of most analysts, placed the Dutch brew firmly in the shadow of Interbrew's top-selling premium lager Stella Artois.
Unlike the rest of the world, Heineken in the UK is not a premium strength lager.
It was launched as a standard lager in the 1970s, before the public acquired a taste for stronger brews such as Stella Artois and Kronenbourg.
Kevin Baker, beer analyst at Canadean research, says: "Heineken is a value for money brand in the UK. It is right down there with Skol and other cheaper lagers.
"It was never going to sit comfortably in the Interbrew portfolio.
"Any move upscale would bring it into conflict with Stella.
"It could maintain the status quo but I think, in the end, they (Heineken) would reach the stage where they have to re-position the brand or quit the UK altogether.
"Buying Bass will give them a strong base to re-position the Heineken brand as a premium lager."
It is unclear at this stage if the DTI will force Interbrew to sell Bass's interests in the Czech Republic, where it owns the number two beer Staropramen.
If Interbrew was allowed to hang on to Staropromen, it would be small consolation in what has been a costly and time-consuming contest.