Everton are short at full-back as captain Seamus Coleman is dealing with a calf issue, Nathan Patterson is out for the long term and Ashley Young is suspended after being sent off against Brighton.
Midfielder James Garner, who can fill in at right-back, is also out so teenager Roman Dixon could be drafted in, while James Tarkowski is a doubt and fellow centre-back Jarrad Branthwaite continues to recover from a groin problem and is “not close” to returning.
“It is still an ongoing challenge,” said Dyche. “We have not got much financially to correct the situation. We have just got to work with the players and hope their fitness gets back to being fully fit and then staying fit.”
Everton have spent around £40m on new signings this summer, while recouping in the region of £70m by selling Amadou Onana, Lewis Dobbin and Ben Godfrey.
It is understood any further arrivals in the remainder of the transfer window would probably be on loan deals.
Asked if the club expected to be busy before the deadline on Friday of next week, Dyche replied: “I think that is unlikely.
“We worked very hard in the market and brought in players who we think can develop into the Premier League. They are not all game-ready straightaway, but we think they are good players that can grow into the club.
“Working very hard to get those deals done then losing players as well, there is not much more wiggle room. If there is, then that is helpful, but if there is not then that is the way it is.”