It is understood Paragon has requested documentation relating to the sale with a view to making an offer.
The sale is expected to return around £1bn of the £1.4bn invested in the failed institution by the taxpayer.
Paragon joins Coventry building society, Virgin Money, Co-op Financial Services and NBNK as bidders for the assets.
The lender narrowly avoided a similar fate to Northern Rock after going cap in hand to investors after the financial crisis hit.
It was forced to stop lending between 2008 and 2010 but has since rebounded, with strong demand for rented accommodation helping push profits up.
Pre-tax profit for the six months ending in March rose 34.8 per cent to £39.5m, and the company also raised its interim dividend by 12.5 per cent to 1.35p.
It says it expects further growth in lending for the rest of the year.
George Osborne confirmed the sale would go ahead at his Mansion House speech last month.
Both the Treasury and Paragon declined to comment on the sale.
The Northern Rock sale is expected to take place after the sale of 632 Lloyds branches.
FAST FACTS | NORTHERN ROCK SALE
● Analysts expect the sale to net between £650m and £1bn. High capital requirements are expected to lower the value.
● Paragon has bounced back in the wake of the recession, when it was forced to make a cash call. It resumed lending last year.