Enterprise, a Preston-based support services group, is also in the frame.
Sources say the deal, thought to be worth up to £15m, is nearing completion after dragging on through the summer. Speedy Hire, formerly called Allen, is understood to want the deal finalised by the time it announces its results on 29 November.
A source close to the deal said Alfred McAlpine, Balfour Beatty and Enterprise were favoured to clinch Ryan out of an original field of 12. The way for the sale has been cleared after Speedy Hire settled long-running contractual disputes with a major client, which the firm refused to name.
The source said: "Ryan is a good company, operating in a good sector, and has excellent contracts now disputes have been resolved. Whoever buys it will have got themselves a great operation."
He added: "It would fit with what McAlpine wants very nicely."
Speedy Hire will only say that negotiations are going well, and that it hopes to have finalised the deal by Christmas.
McAlpine has emerged as a favourite since it sold its homes arm to Wimpey for £461m earlier this year. The company said at the time that it would use some of the cash to strengthen its support services businesses and could eventually spend up to £200m doing so.
Oliver Whitehead, chief executive of McAlpine, refused to confirm whether his company was still in the running, but said it had considered buying Ryan when it first went on sale.
He said: "We had a look, but at the moment we have people offering us companies all the time. It started as soon as we sold the housebuilding arm and people realised we had a bit of a cash to spend."
Whitehead added that Wimpey was paying for the housebuilding division in installments over the next year. "So we haven't got all that cash to spend."
Balfour Beatty also has a big warchest and is known to be looking at the utilities market. The company refused to comment.
Speedy Hire sold off its contracting businesses to YJL earlier this year after it decided to focus on its more lucrative plant hire businesses. The firm's sheet piling, scaffolding, housing and civil engineering businesses have also been sold.
