Warnock was frustrated when attempts to bring Joel Ward to the club were scuppered and the former Portsmouth youngster opted to join Crystal Palace instead.
But any thoughts of leaving Elland Road were banished when Warnock's son reminded the 63-year-old just how much he wanted to win promotion with Leeds.
Warnock told the Yorkshire Evening Post: "I was disappointed to lose Ward to Palace earlier on in the summer; in fact at that stage I'm not sure I was going to be here.
"There were temptations and I think it might have been easier to take an offer elsewhere than stay here.
"My son James lives here and he's the one that over this summer - when it would have been easier to leave - who has pleaded with me to give it a go.
"Because he knows how desperate I am to get another promotion."
Warnock also identified the Leeds fans as a factor in his decision to continue because of their committed support - even during a 7-3 home defeat to Nottingham Forest in March.
He added: "I'll never forget the fans' support here last season. The one thing about the fans since I've been here is that they have been magnificent.
"I'll never forget the Forest game at home in the last ten minutes of that game when I was talking to Ronnie Jepson (reverse team coach) and saying: 'Let's put something on this pitch next season for this lot to get excited about.'
"And that's what I'm trying to do."
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