The two groups, who are both involved in bid talks with Omega, held talks recently at the Reinsurance Rendezvous in Monte Carlo, a conference for the reinsurance sector.
The talks broke down but yesterday sources close to Byrne said he had not ruled out an amalgamation at some further point down the line.
Byrne’s Haverford vehicle yesterday issued a tender document aimed at gaining a 25 per cent holding and management control at Omega. He did so without regulatory approval, which he hopes to get in November.
Barbican, which has raised £105m in recent years from Carlson Capital and Steel Partners, has proposed a reverse takeover of Omega. The group, which specialises in marine, aviation, and property reinsurance, now has net assets of only £80m, according to industry sources.
The third, but possibly favourite bidder Canopius, yesterday said that the due diligence for its full 84p a share offer would be completed by the end of the week.
Michael Watson, chairman of Canopius, said: “We are encouraged by the feedback from a wide range of institutional shareholders, a significant number of whom have expressed interest in a full cash bid. “
Canopius hopes to launch its bid next month.