BBC bosses are said to have been delighted with the One Show presenter since she took over from Christine Bleakley, and plan to raise her profile by booking her on the reality competition.
According to a source, Jones's handling of former co-host Jason Manford's recent sex scandal particularly impressed execs.
The insider told The Sun: "Alex has been a dream come true for The One Show. She held the whole thing together and everyone's grateful. Bosses think it's her time to shine."
Jones is also lined up to present the third series of Let's Dance For Comic Relief.