Both Short and Sunderland chief executive Martin Bain have been aware of the incident for the past two weeks but no action has been taken. And Moyes believes he has done enough by apologising to Sparks.
At a press conference in the build-up to tonight's Premier League clash at Leicester, Moyes said: 'I deeply regret (what I said) and I've done what I had to do and apologised, which I was right to do so.
'In the heat of the moment, I made a mistake in my comment to a BBC reporter which I profoundly regret. I was disappointed with myself for it. I subsequently phoned the reporter and apologised, which she accepted.'
When asked if he expected to keep his job, Moyes said: 'Yes. I don't see it as being something which is in my character.
'It is something which is out of character. As I said, I've apologised to the girl.'
BBC presenter Gary Lineker said Moyes had treated Sparks with 'utter disdain' and called his actions 'inexcusable', while the domestic abuse charity Wearside Women In Need said they were 'appalled' by his behaviour.
Moyes rejected Lineker's opinion, adding: 'I don't agree. In the heat of the moment, sometimes the questions come in and you can answer them wrongly. You don't always say the right things.'
Moyes has also been condemned by Shadow Sports Minister Dr Rosena Allin-Khan, who tweeted: 'David Moyes cannot get away with these sexist threats - the FA must take action immediately.'
Clare Phillipson, director of Wearside Women In Need, added: 'It is for the FA to set a clear standard about what they think is acceptable. It was dreadful, absolutely appalling.
'This is a woman, in a very small minority of sports journalists, trying to go about her job and being threatened.
'It's the sort of thing you expect down the local pub, not the kind of thing you get from a professional football manager.'
A statement from Women In Football read: 'We are deeply disappointed and concerned by the threatening language used by Sunderland manager David Moyes.
'We are calling on the FA to help educate football managers against this type of behaviour. No one should be made to feel threatened in the workplace for simply doing their job.'
Sunderland are eight points from safety at the bottom of the Premier League and travel to Leicester having won just once since December 17.
Moyes, however, has been assured that his job is safe even if the club are relegated. His reign has been plagued by problems on and off the field since being appointed last summer, but he insists he wants to carry on. 'Yes, I want to do the job and I want to get it right,' he said. 'There's been a lot of difficulties, but I want to be here. This club has not been winning often enough for a long time now.
'It's been a difficult season for lots of reasons, but I believe there are better times to come.'
