The company, which kicked off a strategic review in July after a profit warning and the departure of chief executive Richard Howson, said it has received approaches from “more than one credible counterparty” for a possible acquisition of the business.
Shares jumped 4.94% to 45.65p in afternoon trading.
Carillion wants to sell the business in an effort to strengthen its balance sheet following deterioration in cash flows on some problematic construction contracts.
In September the group booked a further £200mln in contract write-downs to add to the £845mln of provisions revealed in July.
READ: Carillion drops over 12% as says exploring options including a share issue to shore up its battered balance sheet
Interim chief executive Keith Cochrane has said he wants to raise cash by offloading its Canadian and UK healthcare arms.
Canada is the largest component of the two businesses and the group hopes the sale of the business will generate more than £300mln.