Jeremy Clarkson "will be back on the BBC", according to the head of BBC Two and BBC Four.
Kim Shillinglaw, who has the task of finding Clarkson's replacement after he was dropped from Top Gear, said the host had not been banned by the BBC.
"It's serious and unfortunate what happened but there is no ban on Jeremy being on the BBC," she said.
"It's a big deal what happened and Jeremy, as any human being would, needs some time."
Clarkson was removed from presenting duties on Top Gear after assaulting producer Oisin Tymon.
The decision caused an outpouring of support from Top Gear fans, with more than a million people signing an online petition to reinstate him.
The row, which took place in a North Yorkshire hotel, was said to have occurred because no hot food was provided following a day's filming.
After an internal investigation in March, BBC director general Tony Hall confirmed Clarkson's contract would not be renewed.
In his latest Sunday Times column, Clarkson revealed he thought he probably had cancer at the time he hit Tymon.
He said the incident came on his "most stressful day... in 27 years at the BBC" - but added other people facing stress "manage to cope better than I did".
Shillinglaw said it was an "open book" on who might replace the 55-year-old, following rumours it could be a woman.
She said: "We'll definitely look at some women but it's not a driving priority."
The executive also confirmed Clarkson's final Top Gear scenes would be screened later this year
"No way would I want the available material not to be seen by viewers," she said.
However, there is not enough footage to piece together the three remaining episodes of the series, which was pulled off air in the aftermath of the altercation with Tymon on 4 March.
Sue Perkins, the host of BBC One's The Great British Bake Off, was named the bookmakers' favourite to replace Clarkson a fortnight ago.
Bookmakers Coral said she was the front-runner for the job, followed by Dermot O'Leary and Jodie Kidd.
The news prompted a barrage of abusive tweets for Perkins, whose Twitter timeline was filled with "blokes wishing me dead", including threats from someone who "suggested they'd like to see me burn to death".
She later quit Twitter, leading Clarkson's co-presenter James May to suggest those who sent the abusive tweets should "do the world a much bigger favour by killing yourself".
"Obviously I don't actually want people to kill themselves but, really, we don't want them as fans," May added.