The winner of the Swansea licence will gain access to more than 300,000 listeners in the Welsh coastal city while the successful group in the Northallerton area of North Yorkshire will have a potential audience of 30,000.
The Wireless Group is likely to bid for both stations with AllTalk FM, its recently acquired Edinburgh FM station, as the company's strategy is to create a local speech-radio brand across the UK to challenge the BBC's dominance.
GCap, the merger of Capital Radio and GWR will be finalised on Monday, is also expected to be interested in the licences.
Radio giant Emap and Jazz FM-owner Guardian Media Group have already separately confirmed they will not be tabling bids for either of the licences.
Chrysalis, owner of Heart FM, was unavailable for comment at time of going to press.
The deadline for applications is August with the winner to be announced in the autumn.
The news comes as the winner of the coveted Manchester FM licence is expected next month. GCap, Emap and The Wireless Group are still in the running after Guardian Media Group pulled out in February.
Applications for the south-west Solent commercial licence are also due in this week.
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