BICC shares have rallied to about 90p from a 52-week low of 38p, but are still well below the 180p they stood at a year ago. The firm is also under pressure from aggressive conglomerate Wassall, which took a 9.3% stake in it late last year.
Analysts believe BICC will use its annual results announcement on 10 March to boost market sentiment, with a demerger of the firm's cables business possible.
BICC announced on Monday that it is selling its Telecommunication Cable business for $133m (£84.7m). Analysts believe that this signals a move to concentrate on construction.
Such a move would represent a major turnaround for BICC, whose cables business carried the Balfour Beatty contracting arm through the construction recession of the early and mid-1990s before subsequently falling on hard times itself.
One senior City source said: "It's very possible that BICC could become Balfour Beatty by getting out of cables altogether and investing the proceeds in the construction business.
BICC could become Balfour Beatty by getting out of cables and investing in the construction business
Senior City Source
"Because the cables arm is doing badly, it wouldn't be a great leap to make the divestment, and, to the right buyer, it might be a good deal to take capacity out of that market.
"What we would urge, though, is to dispose of the cables arm all at once. Selling piecemeal would be unsatisfactory." Another analyst said: "BICC is under real pressure to do something, but there would be a question mark over the financing of Balfour Beatty if it became part of a smaller group.
"There's also the question of time. Could BICC move quickly enough to head off a possible bid from Wassall? Tarmac's demerger of its construction and aggregates businesses is going to take nine months," he added.
Another analyst said he expected Balfour to report impressive results that would make the firm an attractive proposition to investors.
In 1997, Balfour lifted operating profit from £10m to £42m. This year's results are expected to be similar, buoyed by a strong performance in the rail sector.