The presenter, who joined Channel 4's youth strand in 2009, is said to have impressed bosses after recording a series of pilot shows for the station.
Jamil has also had trials with fellow T4 presenter Matt Edmondson, who already presents a Wednesday night show on BBC Radio 1, The Sun reports.
Radio 1's acting controller Ben Cooper wanted to see if the pair have the right chemistry and was apparently pleased with the results.
An insider said: "Ben seems really impressed. I wouldn't be surprised if they get her in at some point to cover a slot when one of the DJs is off."
BBC Radio 1 confirmed: "We can confirm that Jameela has been doing pilot shows. We are always trying out fresh talent that appeal to our young audience."
T4 presenter Nick Grimshaw also hosts his own Radio 1 show, as does former T4 host Vernon Kay.
Watch our interview with Jameela Jamil below: