Banking sources believe a bid is imminent from the consortium which has already said it will offer not less than €20.75 for the shares if it decides to make a formal offer to buy the shipping company.
Last Friday the takeover panel set a deadline of June 13 on a bid for the group which owns and operates Irish Ferries.
Both groups have been in talks with ICG since April and have carried out extensive due diligence on the group.
They have already indicated their willingness to pay at least €20.75 a share for the company, well ahead of the management buyout offer (MBO) which valued the shares at just €18.50 each.
The MBO was led by ICG chief executive Eamonn Rothwell who has headed the company since it went public in 1988.
Since One51 and the Cork-based Doyle shipping group indicated their intentions of bidding at least €20.75 for the shares, the MBO offer — which has the backing of the independent directors — became redundant.
Mr Rothwell and other senior managers offer of €18.50 to buy the group, valued the company at €471m including €100m debt.
In early April the joint bidders, who had been stake-building in ICG, said it was possible they could offer over €20 per share for the group once it had carried out due diligence which is now “substantially complete”.
In the meantime they bought shares at prices of up to €20.75 in ICG and any bid will have to be at that level or higher, under stock exchange rules.
A share price of €20.75 values the group at well over €500m.