Building revealed in September that Sisk was in negotiations with several large construction firms in Cardiff, Bristol and the South-west.
Sisk was understood to have spoken to Cowlin Construction and Pearce Construction of Bristol, Midas Construction of Kingskerswell near Torquay and two firms in Cardiff.
One insider said Sisk had been carrying out due diligence over the last couple of weeks and was now close to completing the deal.
The insider said the contractor had begun a consultation exercise with employees.
The insider added: "There will also be a large recruitment drive within the firm in the new year to recruit people from Bristol and the local surrounding area to work in an expanded business."
Sisk managing director Pierce O'Shea told Building in September that he had employed a corporate finance firm to look at a range of companies in the Bristol area.
There will be a big recruitment drive within the firm next month
He said: "We as a company have agreed that we want to move into the Cardiff and/or the South-west region. Where we move into depends on which firm we acquire, which has the best fit with us as a company."
The Bideem Group has its headquarters in Avonmouth, Bristol, with regional offices in Caerphilly and Theale, Berkshire.
The group has a range of companies and divisions specialising in building, civil engineering, plant hire and mechanical and electrical services.
John Sisk has bases in Ireland, the UK and a number of African countries. It is the largest general contractor in Ireland with a turnover of more than £500m.
Clients include Hewlett Packard, IBM and Coca-Cola. It has also completed facilities developments in Ireland for leading pharmaceutical and electronics companies.