Riley, who left his role as Chrysalis Radio chief executive after Global finished its acquisition of the company, is working with Vitruvian.
Global has been seen as the strongest bidder because it has the cash to pay for Emap Radio, which includes station networks Magic and Kiss, outright, while private equity bidders are reliant on debt.
The second round offers are due in towards the end of the month.
GCap Media submitted a first round offer but it is not clear whether it is still in the auction according to the Telegraph.
Separately, Emap this morning said it is inviting bidders for its business-to-business division to buy Emap plc in the event that the auction results in the B2B division being the only business left within Emap plc.
Emap said: "This is being proposed purely as a possible way of enabling the return of the cash, including the proceeds of any potential disposals, to shareholders in an efficient manner."
Making the announcement means that under the City's takeover and mergers code, an "offer period" has commenced.
The list of bidders for the £1.5bn-valued B2B division includes Guardian Media Group and Apax in partnership, Candover, Providence and Cinven. The Telegraph said its sources are speculating Reed may be carrying out due diligence on the division.
Emap's B2B titles include Broadcast, Drapers Record, Construction News and Local Government Chronicle.
Earlier this week, it was reported that Cinven has dropped out of the running for Emap's consumer magazine division, leaving less competition for Hearst, which if successful would merge the business with its The National Magazine Company business in the UK.
Emap today said it continued to be encouraged by the progress of the auction confirmed that no bidder has come forward with an approach for the company as a whole.
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