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According to the Daily Mail, the former Blue Peter host will be tested out with a guest stint on the magazine programme within the next few weeks.
Sources say that the 32-year-old is "likely" to secure the position if his trial run gets a positive response from viewers.
It is thought that bosses believe Baker has a "light-hearted touch" which would make him well-suited to the job.
Chiles last month quit The One Show and his other BBC projects in favour of a new four-year deal with ITV.
Richard Hammond and Matt Allwright are among other presenters who are said to be in the running to replace Chiles.
