The BBC Radio 2 DJ is said to be on a list of household names who will be offered a deal to join the lineup of the upcoming tenth series.
Evans has however allegedly stalled contract talks after expressing an initial interest in appearing on Strictly, reports The Sun.
"Chris would be a brilliant signing," a source said. "He is a TV legend and would bring his own brand of humour and charisma to the show, not to mention nine million Radio 2 fans and five million One Show fans.
"Nothing is confirmed yet, but we have our fingers crossed."
Evans's signing is said to be an opportunity to improve the ratings of The One Show, which he co-hosts on Fridays with Alex Jones,
Jones took part in Strictly Come Dancing last year, partnered by James Jordan.
The insider added: "Alex was worried about going on Strictly, but loved every minute and has told Chris how much fun it was. The bosses hope her encouragement will swing it."
Snooker star Ronnie O'Sullivan and Coronation Street's Michelle Keegan have also been tipped to feature in the next series.