Managing director Philip Hunt confirmed the company was seeing a shortlist of six agencies before deciding which to hire in the coming weeks.
The company, which used consumer tech agency Nelson Bostock until a year ago, has worked with Xavier Adam Public Relations since then.
Agency founder Adam is understood to have submitted a proposal for the work, but is joined on the pitchlist by five other firms in sectors in which Wheel's clients operate.
Hunt said the agencies he had chosen to pitch, which he refused to name, had been 'an eclectic mix of firms through both personal recommendations and client sector specialisms.'
The new media firm restructured three months ago into 'vertical' business categories - it now boasts specialisms in financial services, retail and entertainment and luxury goods areas.
It also last week announced the acquisition of the brand name of online marketing agency Abel & Baker, which it will maintain as a standalone brand.
'We decided with the changes that we needed a radically different message to put out so we rebriefed Xavier and invited other PR firms to tender,' Hunt said.
The brief will focus on corporate and B2B work for Wheel, which turned over just under £15m last year, a 68 per cent increase on the year before.
'Our sector has had a pretty rough time but we feel the upswing is about to come. Our experience of the last major growth phase was that recruitment became increasingly problematic,' said Hunt.
'We hope to use PR to ensure that we are perceived as a thought-leader when the upswing arrives, so people want to come and work for us,' he added.