The England international, who has won four caps under Gareth Southgate since making his debut against Costa Rica in 2018, has been in excellent form this season.
Following some jittery performances by Hugo Lloris, Spurs have reportedly been considering a move for Pope this summer, viewing him as a potential long-term replacement.
Burnley have previously been forced to cash in on their most valuable assets, such as Kieran Trippier, Michael Keane and Andre Gray, to keep the club on a stable financial footing.
But Dyche is now a more bullish mood, believing that the recent takeover by ALK Capital will enable him to hold onto his best players for longer, or else command higher fees for them.
According to LancsLive (opens in new tab), when asked what sort of fee it would take to sign Pope, Dyche jokingly responded: “How do you know every offer would have to be massive?
“If they offered a bag of crisps, a pint of lager, in a pub, at the moment with the way things are going, I might be swayed. I might actually take it.
“If someone can find a way of changing the rules of the country, get me a pint and a big of crisps then I will have to try and hang on to Popey the best I could.”
Pope has conceded just 25 goals in 24 games for Burnley this season, keeping nine clean sheets in the process.
His contract runs until June 2023, with the option of a further year, meaning that a substantial fee would be required to convince the club to sell.
Spurs' current back-up goalkeeper is Joe Hart, who left Turf Moor last summer after just 19 appearances in the Premier League during his two years there.
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