If the sale goes ahead it will create one of Europe's top five construction companies, with a combined turnover of £4.4bn.
Analysts described the bid, announced on Wednesday by the Dutch contractor and housebuilder, as surprising, because Heijmans is one-third the size of HBG. The feeling was, however, that it had a good chance of succeeding.
One said: "It looks a pretty smart move by Heijmans. It has been sniffing around the UK for some time. The deal would be a big step but I'm optimistic."
HBG's shares have suffered since it bought German contractor Wayss & Freytag in 1996. The group made a net loss of £41m for the year to 31 December 2000, mainly because of bad results in Germany. Its share price rose 18% after Heijmans announced its bid on Wednesday.
Adrian Franklin, chief executive of HBG UK, said that the proposed merger would not affect his company.
He said: "From our point of view, we don't see it has any effect. We will carry on and that is what we are doing." The UK arm of HBG has a turnover of £919m.
An HBG spokesman in the Netherlands said: "We are considering our answer to Heijmans. We will make further statements as soon as it is clear what the answer will be."
Last year, HBG promised to support the UK arm's plans to increase its PFI portfolio by 20%. Its PFI projects are mainly courts, hospitals and schools.
Analysts said that the decision to put in a bid for HBG was part of a general consolidation of European construction market.
One said: "It's a significant move. You could see another household name disappearing. They seem to be dropping like flies. Consolidation is really beginning to gather pace in construction."