Pope had an operation to address a cartilage problem, which ruled him out of the Clarets' last three games of the season, and England's Euro 2020 campaign.
And Dyche is looking forward to seeing the 29-year-old back in top form next season.
Dyche said: “We’re expecting the recovery to go well at this early stage, but we’ll wait and see as he recovers.
“He’s had a really, really good season once again.
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“He continues to develop into a top, top keeper.
“He’s incredibly unfortunate to have this happen at this time but once again he’s shown what a top keeper he is during the season and I’m sure will do again going into next season once he recovers.”
Pope started England's last three games, with Jordan Pickford ruled out through injury in March, and was pushing the Everton keeper hard for number one jersey, with three keepers in the Premier League keeping more than Pope’s 11 clean sheets during the season.
Three Lions boss Gareth Southgate said yesterday after naming his provisional squad: “For Nick, it's heartbreaking to get an injury so close to a major tournament.
“He's been a fantastic member of our squad; a totally unselfish guy.
“In Russia, he spent hour after hour throwing himself around for penalties, which was as important in our penalty shoot-out success as the guys who took them.
“Him and Jack Butland were phenomenal in those situations. I'm really disappointed for him.”