US Edition Sources said Blackstone has been appointed to negotiate with Citigroup, which is trying to offload Enterprise's debt to several "loan-to-own" funds.
Citigroup advised and provided debt to 3i on its £500m acquisition of Enterprise in 2007, the height of the credit boom.
Banking sources claimed a potential argument is brewing between 3i and Citigroup over the syndication of Enterprise's debt. Although Citigroup is said to have found buyers for Enterprise's debt at a discount price, the loan agreements stipulate that 3i and Enterprise have the final say on whether the debt can be sold off.
It is thought 3i and Enterprise are wary about the potential buyers, especially as some are said to be "vulture" funds, such as Varde, the American hedge fund that recently bought a huge portion of UK housebuilder Crest Nicholson's debt.
Reports claimed other buyers of Enterprise's debt could include rival private equity firms KKR and TPG Capital. Goldman Sachs was also tipped as another potential acquirer of the debt.
A person familiar with the situation tried to play down the possibility of a disagreement between Citigroup and 3i: "3i and Enterprise just want to ask a few questions about who the buyers of the debt are before it is sold."
3i recently appointed Alan Peterson, a renowned 'company doctor', to shake up Enterprise following a tough period of trading. Mr Peterson, the former head of HSS and Jewson, is one 3i's most trusted operators.
3i declined to comment.