Bradford co-chairman Mark Lawn does not think Sunderland or Fulham will fancy the trip to Valley Parade in the fifth round of the FA Cup.
Monday night's draw pitched Chelsea's unlikely conquerors into a home tie with either Gus Poyet's Premier League Black Cats or Kit Symons' Championship side, who are due to replay next week after a 0-0 draw on Saturday.
"We're at home, I think we can win at home," he told Sky Sports News. "They won't want to come down here and get this lot (the fans) bouncing. I don't think Sunderland or Fulham will want to come to Valley Parade."
City's 4-2 win at Chelsea - having been 2-0 down to the Premier League leaders - is already one of the cup's greatest upsets and another feather in the cap of manager Phil Parkinson.
The former Charlton boss oversaw Bradford's run to the League Cup final in 2013 and earlier this season took the scalp of Leeds in the same competition.
Lawn, though, is confident that his man will stay at the helm despite the interest he is likely to generate.
"He's got 18 months left to run and we don't want him to go anywhere," he added. "I think he's a bit rubbish, so all the other teams, keep your bloody hands off!"
City last faced Sunderland back in December 2003 where they lost 3-0 with a side containing the likes of Wayne Jacobs and Dean Windass. Their last meeting with Fulham came further back in 1994, a 0-0 draw.
Bradford were not the only side to cause a shock at the weekend, with Middlesbrough's 2-0 win at Manchester City equally worth of praise. Aitor Karanka's Championsip high-fliers will now head to holders Arsenal, who beat Brighton on Sunday.
League Two Cambridge, who held Manchester United to a home draw, head to Old Trafford next week with the winners headed for a clash with Sheffield United or Preston.
On Monday night Stoke won 4-1 at Rochdale to lay on a meeting with Blackburn, manager Mark Hughes' former club.
"It will be good to go back," said Hughes. "I have good memories of my time there and there are lots of people I know still there."
Hughes admitted the fear of an upset drove his side on and said: "I mentioned what happened to the players over the weekend before the match. It would have been foolish not to.
"There was a reason why the television cameras were here - people were hoping for an upset, but we didn't want to be a part of that."
Liverpool and Bolton will replay for the right to go to Crystal Palace, while Leicester and Aston Villa meet in a Midlands derby. West Brom face West Ham at home and Derby play host to Reading in an all-Championship affair to round off the draw.
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