Laing O'Rourke is also expected to be interested in parts of Mowlem if any new owner decides to break up the company.
Analysts believe a bidder would have to pay around 225p a share, valuing the company at £320 million.
One construction chief executive said: 'It has to be overseas money coming in - I can't see anyone in the domestic market being interested at that price.'
And a leading City analyst said: 'Maybe they could get that figure if a big European contractor came in.'
The approach follows a torrid year at Mowlem. Chief executive Simon Vivian reviewed over-optimistic forecasts on the firm's contracts, leading to a round of job cuts and a profit warning.
One analyst said: 'The feeling is that Vivian has come in, dealt with the problems and booked the pain and now the company can move ahead.'
Mowlem has an impressive order book, including a £492 million motorway widening contract on the M1. It is also preferred bidder with joint venture partner KBR on the £5 billion Allenby and Connaught PFI job for the MoD.
A source close to Mowlem said: 'The PFI side would be attractive to European buyers and the major projects and civil engineering operations are good business.'
Building head David Limming was heading the Allenby project but is leaving to join Carillion in the New Year.
A source close to Laing O'Rourke said: 'There are a lot of bad jobs at Mowlem but some parts of the business are attractive. O'Rourke is always in the market for a bargain.'