Spurs are winless in their last 13 Premier League fixtures and sit 17th in the table, just a point above the bottom three with seven games remaining, the first of which is at the Stadium of Light on Sunday.
Dyche was one of the names linked with replacing Igor Tudor after the Croatian’s short, calamitous reign but told talkSPORT on Tuesday he never held talks with the club.
Instead they appointed former Brighton man De Zerbi and Dyche expects to see a badly needed upturn in form.
“Tottenham have bottomed out, I’m sure, which means they can only get better,” he told the radio station.
“I’d be amazed if they don’t have a bounce. But I don’t think you can call it (the relegation battle). I have no clue who’s staying up.”
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Former Burnley and Everton boss Dyche, who was sacked after 18 games in charge of Spurs’ fellow strugglers Nottingham Forest earlier this year, had been touted as a short-term fire-fighting option for the London club.
And, while he suggested the idea did not appeal to him, he offered some advice to De Zerbi about what would be needed to stay in the top flight.
“For me it would be: strong, fit and organised. That keeps you up, not just relying on talent,” he said.
“What’s the framework of the side? What’s the energy, what’s the output? What’s the hard yards and how much of those are you putting in?
“You are going to find it very hard to stay in the Premier League if you don’t get the framework and the basics right.”
Reflecting on the concerns he would have harboured had Tottenham approached him, Dyche added: “I wouldn’t go in there looking for money.
“They could offer me a massive amount of money, I’m sure they’re capable of it, and allegedly they’ve offered De Zerbi a massive amount of money. It would have been about what are you going to help me gain as a human being. What would I gain?
“Let’s say you go in there and get the job done, then next season if you’re not in the top four and the football’s not what they want, then you’re rubbish and they want you out. If you don’t get the job done, then somehow it’s on my neck that I took Tottenham down.”
De Zerbi insists Tottenham have enough to get out of trouble - but says he's in it for the long haul regardless.
“I signed five years of contract because, for me, it is a big challenge and I will be the coach of Tottenham next season, no matter what,” De Zerbi said.
“It’s a difficult moment for everyone at Tottenham but I think we have the right qualities to come out of this moment.
“I believe in the players. I think we have to remember who we are and who the players are, because we have very big players and we have to work on their confidence and qualities.”
Sunderland are preparing to return to action after their three-week stoppage following the derby win over Newcastle.
The break has given a number of key players the opportunity to work their way back to full fitness after injuries, and the likes of Nordi Mukiele, Reinildo and Enzo Le Fee are all in contention to start on Sunday.
Regis Le Bris will update on Dan Ballard's situation when he speaks to the media on Friday. The centre-half missed the Newcastle game and was forced to withdraw from the Northern Ireland squad after picking up an injury in the defeat to Brighton the last time out at the Stadium of Light.