The news came as the management of Driver Construction, which will be the subject of a winding-up petition next week, attempts to avoid being forced into liquidation.
The acting managing director of the firm, Dean O'Connell, will argue that creditors will be best served if the firm could go into administration and continue trading.
O'Connell has been obliged to take this step after a creditors' voluntary agreement put forward by Driver's management was rejected by creditors last Wednesday. Creditors were being offered 67p in the pound by John Aviss, the owner of Driver.
The SFO has been examining the circumstances of Bickerton's collapse since January last year. Bickerton was sold to Aviss in 2001 as part of a series of deals with Artisan, a developer listed on the alternative investment market.
Inspector Bill Matthews of Cleveland police, has been conducting a joint investigation with the SFO into the collapse of Bickerton. He said he was aware of the difficulties that Driver faced.
"We will be looking at the Driver situation to see how it may relate to our investigation into Bickerton Construction," he said.
We will look at Driver to see how it may relate to Bickerton
Matthews emphasised that a full-blown investigation had not yet been launched into Driver Construction, but that the situation was to be discussed at a meeting with the Serious Fraud Office next week.
It is understood that the police have interviewed a number of creditors of Driver Construction, including London developer MacNiven & Cameron, one of the firms that rejected the creditors' voluntary agreement.
MacNiven & Cameron refused to comment.
O'Connell said he was aware that Macniven & Cameron had held talks with the SFO. He said Driver faced a winding-up petition from one of its creditors, builders merchant Travis Perkins, and that he was preparing a case for putting the company into administration. O'Connell expressed confidence that the firm could trade out of its difficulties.
O'Connell said that he had been involved with Driver Construction for five weeks. He was given the job after answering a recruitment advertisement for a managing director in the London Evening Standard.
O'Connell said he felt Driver Construction had some salvage value as there was money in the company. He said: "The company has been poorly managed for the past 18 months but I came here as I felt that I could turn it around."
He said that he had nothing to hide and had already contacted the SFO to see if he could be of assistance.