In November, Councillors unanimously rejected the application to establish the facility near Glasgow Airport.
Proposals by Arora Management Services included developing a 20-bed facility, featuring ancillary accommodation, which the Home Office would have used as a short term holding facility. However, the application was rejected as it was contrary to the area's local development plan.
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Council Leader Mark Macmillan said there was "clear concern" the facility would be "detrimental" to the Glasgow Airport Investment Area's economic development.
"We are pleased the Home Office has accepted the decision made by councillors and will not seek to have it overturned," he said.
"There was clear concern the proposed facility would be detrimental to the economic development of the Glasgow Airport Investment Area, which is one of the key economic drivers both for Renfrewshire and our wider Glasgow City Region.
"Members of the Planning and Property Policy Board agreed that there was no established identifiable functional link between the proposal and the airport's operations.
"The proposed facility's location in a commercial and industrial area would also have introduced an inappropriate use through the attendant noise, activity and disturbance."
(LM)
