Private equity firms Exponent, Bridgepoint Development Capital and TA Associates are among the firms chosen to enter the second round of bids due in April, according to reports.
The first round of bids attracted up to 20 indicative offers last month. It is unclear if Lloyds Development Capital is still in the frame to acquire the 47-store retailer.
Isis, Phoenix Equity Partners and Graphite Capital are no longer believed to be in the running.
Hobbycraft has been valued at £75m, but it is now thought it could fetch up to £100m. The retailer has few direct competitors and has been cited as having the potential to grow from 48 to 180 stores.
Despite an initial interest, it is thought Halfords did not enter the first-round bid, but it is unclear if it has since held talks with Grant Thornton, which is running the sale.
It is likely that whoever buys the retailer will retain the current management team, led by Chris Chrombie, the chief executive.