But he did not. Instead, the former Blades manager merely exchanged greetings with the striker whose goals for West Ham United during the run-in five years ago saved the Londoners at the expense of the South Yorkshire club.
Warnock could not, though, resist aiming a few choice words in the direction of his old foe.
“He had this big smile on his face,” said the Leeds chief, who lost his job at Bramall Lane in the wake of the club being relegated and before the Blades were subsequently awarded millions of pounds in compensation from West Ham for breaking rules when playing Tevez that year.
“I told him, ‘You cost me £1m, thank you’. I think he understood.”
Asked by the Yorkshire Post if he still felt bitterness towards either West Ham or Tevez ahead of today’s first meeting with the East London outfit since that fateful season, Warnock replied: “The matter was dealt with and Sheffield United came out of it very well financially.
“Unfortunately, I never got a penny and that rankled with me probably more than Tevez.”
On going head-to-head with the Hammers again, Warnock added: “What happened was nothing to do with the fans. I love West Ham as a club. It is a great club and I have got some friends who are season-ticket holders coming to the game – no doubt they will be coming in my office after.
“I have been in London for the last few years and nothing has happened to change my mind that West Ham is a fabulous club.”
West Ham arrive at Elland Road boasting the best away record in the Championship, the 17 games played by Sam Allardyce’s side on the road having yielded 33 points.
Despite that, the Hammers sit outside the automatic promotion places – something that Warnock feels can only add to the pressure being felt by the London club.
He said: “When you have got a wage bill like they have and the money they have spent, it does put more pressure on you to keep getting results each week. And Reading haven’t helped.
“But I still expect West Ham (to go up). Having said that, of all the top three clubs, everyone would expect West Ham to finish top of the pile.
“You have got to have a bit of luck, too, let’s be fair. You can’t say Southampton didn’t have their share against us. But you need luck at the top of the table – to win games you shouldn’t win and get draws when you should lose.
“With West Ham having such a good away record, it is going to be a massive test. They have drawn the last four at home and they will be glad to get back on the road.
“They don’t have to worry about how they play away from home, they can just get on and do the business. I think that is why they have done so well away from home.
“I am looking forward to pitting my wits against a team of West Ham’s stature. It whets the appetite, especially with the crowd we should have inside Elland Road.”