The 27-year-old was linked with a move to Newcastle United earlier this summer, but a switch to St James' Park has ultimately failed to materialise.
Calvert-Lewin has since attracted interest from other Premier League clubs including Manchester United, West Ham United and Crystal Palace.
It is understood that Everton are yet to receive any concrete offers for Calvert-Lewin, who has entered the final year of his contract at Goodison Park.
Nevertheless, Dyche has insisted that the Toffees can ill-afford to lose the striker for free next summer and a decision must be made soon on his future.
Dyche comments on potential Calvert-Lewin exit
During a press conference ahead of Everton's Premier League opener against Brighton & Hove Albion on Saturday, Dyche was asked how the Toffees would respond if they receive an offer for Calvert-Lewin, who has scored a total of 68 goals in 247 appearances for the club across all competitions since joining in 2016.
Dyche replied: "That would be the challenge for the club - what level (of fee)? For any player, not just Dom.
"You saw Amadou [Onana] leaving us [for £50m to Aston Villa]. There was a level where they think: 'Right that's it, it's got to be done'. That is the current situation of the club. It's not just about the players mentioned, it's about any player.
"The club has got an outside picture and that's not something I can control. They do need to balance the finances better. We have done a lot of work with that since I've been here."
Amidst the club's ongoing ownership and financial issues, Everton have been keen to balance their books during the summer transfer window, with the likes of Onana, Ben Godfrey, Lewis Dobbin and Andre Gomes all departing to reduce the club's wage bill.
Dyche admits Everton are becoming a selling club
Dyche has admitted that Everton can now be considered as a "development" club who intend to make profits from player sale, rather that fork out significant sums of money on big-name signings.
"On the playing side of things to lower the wage bill, we've done a pretty fair job of that. But the bigger picture at the club is dependent on what money is needed at any given time," said Dyche.
"The growth of the team and development of individuals is important for the club. It was once a buying club and now it's not, so now it is development and winning and bringing it all together in a package that can suit the club and be successful, which can be a hard task of course.
"From my point as management it is looking at the players individually and their development, from the club's point of view it is managing the finances as best as possible and from the fans' point of view it is getting as many points and getting up the table."
Will Calvert-Lewin leave Everton this summer?
If Everton become aware that Calvert-Lewin is increasingly unlikely to sign a contract extension, then they will presumably look to sell him before the transfer deadline on August 30, but it remains to be seen whether either Man United or West Ham will be willing to table an offer.
Both clubs are believed to be prioritising additions in other positions at present having already strengthened in attack, with Man United signing Joshua Zirkzee to provide competition for Rasmus Hojlund and West Ham recruiting Niclas Fullkrug to rival Michail Antonio for a spot up front.