The pair - who finished second and 11th respectively in last year's series - are among the stars being considered to judge the BBC contest after Dixon quit for ITV show Britain's Got Talent last week.
Healey is believed to be a firm favourite with Strictly chiefs, while Dell'Olio is said to have been "wooing" executive producer Moira Ross with expensive trips and gifts in her bid to land the role.
"BBC bosses have a shortlist of about eight names and Chelsee is one of them," a source told The Mirror. "She would do really well with younger viewers and help bring in a new demographic.
"As a successful past contestant - like Alesha was - Chelsee will understand exactly what the celebs are going through and bring with her that empathy.
"Bosses have already sounded Chelsee out but Nancy has her heart set on the role. She was one of the main reasons the last series had such fantastic ratings. She believes people stopped watching when she was booted off and thinks her sense of fun and unique personality are just what Strictly Come Dancing needs."
Karen Hardy was named as the early favourite to join the Strictly panel, though Nicole Scherzinger of The X Factor USA and Miranda Hart have more recently been linked to the job.
Dixon's predecessor Arlene Phillips appeared to confess this weekend that she has been struggling to cope with speculation about her return to the show.