The business, which operates both in the UK and Germany, is expected to be sold to CIT for around Â£1.3 billion, according to the Sunday Telegraph, although no sources were cited by the newspaper.
If the deal goes ahead, it will mark the end of an auctioning process said to have included other bidders such as General Electric and Societe General.
The Barclays arm is currently estimated to have assets totaling Â£1.1 billion, with around 60 per cent of this associated with UK business.
Its business involves the arrangement of finance for small and medium-sized companies who wish to invest in new equipment.
So far, Barclays have declined to comment on the reports, although sources suggest that a deal is expected in the next few days.