Paragon, which is worth £600m, is among the parties that have asked for information on the sale of the nationalised bank.
Buying Northern Rock would double its size overnight and enable it to convert into a full-scale bank, reported the Sunday Times.
Other possible bidders include Coventry Building Society, Virgin Money, Co-op Financial Services and banK buy-out group NBNK, it reported.
The sale of Northern Rock was confirmed by Chancellor George Osborne at his Mansion House speech last month.
A spokesperson for Paragon said the company would not comment on speculation.