A project insider said the Home Office was keen to have the centre in operation by the end of the year. Carillion is understood to be on the verge of awarding a £12m M&E package for the scheme to Shepherd Engineering Services.
The scheme, which is to be built on a former Ministry of Defence site between the villages of Arncott and Piddington, was given the go-ahead by the government in July last year, despite fierce opposition from local groups.
Residents in the vicinity of the proposed centre objected to the plans to accommodate asylum seekers, who could travel around the area by day, but would have to sleep at the centre.
Deputy prime minister John Prescott overruled Cherwell council's objections to the scheme, and refused to call in an independent planning inspector.
It is understood that the council is considering a legal challenge to Prescott's decision under the Immigration and Asylum Act 1999.
There is a lot of local opposition; security will have to be reviewed throughout the the project
The insider said the success of the project would depend to a large extent on Group 4's ability to reassure the centre's neighbours that it could guarantee a high level of security.
The insider said: "There is a lot of local opposition to the scheme, so security will have to be reviewed throughout the construction of the project, and also once it is built and being maintained and operated."
The Home Office is considering asylum centres at RAF Newton near Bingham, in Nottinghamshire, and at HMS Daedalus in Gosport, Hampshire.
The Carillion-led team won the Bicester centre against competition from two consortiums, one including Skanska and Premier Prisons and the other led by Interserve and UKDS.